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  • 1.
    Abramowicz, Konrad
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Häger, Charlotte
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Hérbert-Losier, Kim
    Swedish Winter Sports Research Centre Mid Sweden; University Department of Health Sciences, Östersund, Sweden.
    Pini, Alessia
    MOX – Department of Mathematics, Politecnico di Milano.
    Schelin, Lina
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics. Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Strandberg, Johan
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Vantini, Simone
    MOX – Department of Mathematics, Politecnico di Milano.
    An inferential framework for domain selection in functional anova2014In: Contributions in infinite-dimensional statistics and related topics / [ed] Bongiorno, E.G., Salinelli, E., Goia, A., Vieu, P, Esculapio , 2014Conference paper (Refereed)
    Abstract [en]

    We present a procedure for performing an ANOVA test on functional data, including pairwise group comparisons. in a Scheff´e-like perspective. The test is based on the Interval Testing Procedure, and it selects intervals where the groups significantly differ. The procedure is applied on the 3D kinematic motion of the knee joint collected during a functional task (one leg hop) performed by three groups of individuals.

  • 2.
    Abramowicz, Konrad
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Häger, Charlotte
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Pini, Alessia
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics. Department of Statistical Sciences, Università Cattolica del Sacro Cuore, Milan, Italy.
    Schelin, Lina
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation. Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Sjöstedt de Luna, Sara
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Vantini, Simone
    Nonparametric inference for functional-on-scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament2018In: Scandinavian Journal of Statistics, Vol. 45, no 4, p. 1036-1061Article in journal (Refereed)
    Abstract [en]

    Motivated by the analysis of the dependence of knee movement patterns during functional tasks on subject-specific covariates, we introduce a distribution-free procedure for testing a functional-on-scalar linear model with fixed effects. The procedure does not only test the global hypothesis on the entire domain but also selects the intervals where statistically significant effects are detected. We prove that the proposed tests are provided with an asymptotic control of the intervalwise error rate, that is, the probability of falsely rejecting any interval of true null hypotheses. The procedure is applied to one-leg hop data from a study on anterior cruciate ligament injury. We compare knee kinematics of three groups of individuals (two injured groups with different treatments and one group of healthy controls), taking individual-specific covariates into account.

  • 3.
    Abramowicz, Konrad
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Schelin, Lina
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Sjöstedt de Luna, Sara
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Strandberg, Johan
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Multiresolution clustering of dependent functional data with application to climate reconstruction2019In: Stat, E-ISSN 2049-1573, Vol. 8, no 1, article id e240Article in journal (Refereed)
    Abstract [en]

    We propose a new nonparametric clustering method for dependent functional data, the double clustering bagging Voronoi method. It consists of two levels of clustering. Given a spatial lattice of points, a function is observed at each grid point. In the first‐level clustering, features of the functional data are clustered. The second‐level clustering takes dependence into account, by grouping local representatives, built from the resulting first‐level clusters, using a bagging Voronoi strategy. Depending on the distance measure used, features of the functions may be included in the second‐step clustering, making the method flexible and general. Combined with the clustering method, a multiresolution approach is proposed that searches for stable clusters at different spatial scales, aiming to capture latent structures. This provides a powerful and computationally efficient tool to cluster dependent functional data at different spatial scales, here illustrated by a simulation study. The introduced methodology is applied to varved lake sediment data, aiming to reconstruct winter climate regimes in northern Sweden at different time resolutions over the past 6,000 years.

  • 4.
    Frykberg, Gunilla E.
    et al.
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation.
    Johansson, Gudrun M.
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Schelin, Lina
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation.
    Häger, Charlotte K.
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    The Arm Posture Score for assessing arm swing during gait: An evaluation of adding rotational components and the effect of different gait speeds2014In: Gait & Posture, ISSN 0966-6362, E-ISSN 1879-2219, Vol. 40, no 1, p. 64-69Article in journal (Refereed)
    Abstract [en]

    In 3D gait analysis, quantification of leg movements is well established, whereas ameasure of armswing has been lacking. Recently, the Arm Posture Score (APS) was introduced to characterize arm movements in children with cerebral palsy, including information from four variables (APS(4)) in the sagittal and frontal planes. A potential limitation of the APS is that it does not include rotational movements and has not yet been evaluated with regard to gait speed. The aims of this study were (i) to investigate the effect on APS of adding two components of arm rotation (APS(6)) and (ii) to determine the influence of gait speed on the APS measures, when applied to non-disabled adults. Forty-two subjects walked 10 m at a selfselected speed (1.34 m/s), and in addition a subgroup of 28 subjects walked at a slowspeed (0.66 m/s) set by a metronome. Data were collected from markers in a whole-body set up and by eight optoelectronic cameras. The results demonstrated significantly higher APS(6) than APS(4) values for both arms, irrespective of gait speed. Speed condition, whether self-selected or slow, had a significant effect on both APS measures. The two additional arm components are suggested to provide relevant information about arm swing during walking. However, APS(6) needs to be implemented in gait analysis of individuals with gait arm pathologies in order to further examine its utility. Werecommend that gait speed should to be taken into account when using APS measures to quantify arm swing during gait. (C) 2014 Elsevier B. V. All rights reserved.

  • 5.
    Grafström, Anton
    et al.
    Department of Forest Resource Management, Swedish University of Agricultural Sciences, Umeå, Sweden.
    Lundström, Niklas LP
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Schelin, Lina
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Spatially balanced sampling through the pivotal method2012In: Biometrics, ISSN 0006-341X, E-ISSN 1541-0420, Vol. 68, no 2, p. 514-520Article in journal (Refereed)
    Abstract [en]

    A simple method to select a spatially balanced sample using equal or unequal inclusion probabilities is presented. For populations with spatial trends in the variables of interest, the estimation can be much improved by selecting samples that are well spread over the population. The method can be used for any number of dimensions and can hence also select spatially balanced samples in a space spanned by several auxiliary variables. Analysis and examples indicate that the suggested method achieves a high degree of spatial balance and is therefore efficient for populations with trends.

  • 6.
    Grafström, Anton
    et al.
    Department of Forest Resource Management, Swedish University of Agricultural Sciences, Umeå, Sweden.
    Schelin, Lina
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    How to Select Representative Samples2014In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 41, no 2, p. 277-290Article in journal (Refereed)
    Abstract [en]

    We give a formal definition of a representative sample, but roughly speaking, it is a scaled-down version of the population, capturing its characteristics. New methods for selecting representative probability samples in the presence of auxiliary variables are introduced. Representative samples are needed for multipurpose surveys, when several target variables are of interest. Such samples also enable estimation of parameters in subspaces and improved estimation of target variable distributions. We describe how two recently proposed sampling designs can be used to produce representative samples. Both designs use distance between population units when producing a sample. We propose a distance function that can calculate distances between units in general auxiliary spaces. We also propose a variance estimator for the commonly used Horvitz–Thompson estimator. Real data as well as illustrative examples show that representative samples are obtained and that the variance of the Horvitz–Thompson estimator is reduced compared with simple random sampling.

  • 7. Hébert-Losier, Kim
    et al.
    Pini, Alessia
    Vantini, Simone
    Strandberg, Johan
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Abramowicz, Konrad
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Schelin, Lina
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Häger, Charlotte
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    One-leg hop kinematics 20years following anterior cruciate ligament rupture: Data revisited using functional data analysis2015In: Clinical Biomechanics, ISSN 0268-0033, E-ISSN 1879-1271, Vol. 30, no 10, p. 1153-1161Article in journal (Refereed)
    Abstract [en]

    BACKGROUND: Despite interventions, anterior cruciate ligament ruptures can cause long-term deficits. To assist in identifying and treating deficiencies, 3D-motion analysis is used for objectivizing data. Conventional statistics are commonly employed to analyze kinematics, reducing continuous data series to discrete variables. Conversely, functional data analysis considers the entire data series.

    METHODS: Here, we employ functional data analysis to examine and compare the entire time-domain of knee-kinematic curves from one-leg hops between and within three groups. All subjects (n=95) were part of a long-term follow-up study involving anterior cruciate ligament ruptures treated ~20years ago conservatively with physiotherapy only or with reconstructive surgery and physiotherapy, and matched knee-healthy controls.

    FINDINGS: Between-group differences (injured leg, treated groups; non-dominant leg, controls) were identified during the take-off and landing phases, and in the sagittal (flexion/extension) rather than coronal (abduction/adduction) and transverse (internal/external) planes. Overall, surgical and control groups demonstrated comparable knee-kinematic curves. However, compared to controls, the physiotherapy-only group exhibited less flexion during the take-off (0-55% of the normalized phase) and landing (44-73%) phase. Between-leg differences were absent in controls and the surgically treated group, but observed during the flight (4-22%, injured leg>flexion) and the landing (57-85%, injured leg<internal rotation) phases in the physiotherapy-only group.

    INTERPRETATION: Functional data analysis identified specific functional knee-joint deviations from controls persisting 20years post anterior cruciate ligament rupture, especially when treated conservatively. This approach is suggested as a means for comprehensively analyzing complex movements, adding to previous analyses.

  • 8. Hébert-Losier, Kim
    et al.
    Schelin, Lina
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Tengman, Eva
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Strong, Andrew
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Häger, Charlotte
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Curve analyses reveal altered knee, hip, and trunk kinematics during drop-jumps long after anterior cruciate ligament rupture2018In: Knee (Oxford), ISSN 0968-0160, E-ISSN 1873-5800, Vol. 25, no 2, p. 226-239Article in journal (Refereed)
    Abstract [en]

    Background: Anterior cruciate ligament (ACL) ruptures may lead to knee dysfunctions later in life. Single-leg tasks are often evaluated, but bilateral movements may also be compromised. Our aim was to use curve analyses to examine double-leg drop–jump kinematics in ACL-reconstructed, ACL-deficient, and healthy-knee cohorts.

    Methods: Subjects with unilateral ACL ruptures treated more than two decades ago (17–28 years) conservatively with physiotherapy (ACLPT, n = 26) or in combination with reconstructive surgery (ACLR, n = 28) and healthy-knee controls (n = 25) performed 40-cm drop–jumps. Three-dimensional knee, hip, and trunk kinematics were analyzed during Rebound, Flight, and Landing phases. Curves were time-normalized and compared between groups (injured and non-injured legs of ACLPT and ACLR vs. non-dominant and dominant legs of controls) and within groups (between legs) using functional analysis of variance methods.

    Results: Compared to controls, ACL groups exhibited less knee and hip flexion on both legs during Rebound and greater knee external rotation on their injured leg at the start of Rebound and Landing. ACLR also showed less trunk flexion during Rebound. Between-leg differences were observed in ACLR only, with the injured leg more internally rotated at the hip. Overall, kinematic curves were similar between ACLR and ACLPT. However, compared to controls, deviations spanned a greater proportion of the drop–jump movement at the hip in ACLR and at the knee in ACLPT.

    Conclusions: Trunk and bilateral leg kinematics during double-leg drop–jumps are still compromised long after ACL-rupture care, independent of treatment. Curve analyses indicate the presence of distinct compensatory mechanisms in ACLPT and ACLR compared to controls.

  • 9.
    Markström, Jonas
    et al.
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation.
    Grip, Helena
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Schelin, Lina
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Häger, Charlotte
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation.
    Elite women athletes with superior knee function present similar dynamic knee stability, although different movement strategies, when compared to controls2018In: 23rd annual Congress of the European College of Sport Science: Sport Science at the cutting edge, Dublin, July 4-7, 2018, 2018Conference paper (Refereed)
  • 10.
    Markström, Jonas
    et al.
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation.
    Grip, Helena
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Schelin, Lina
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Häger, Charlotte
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation.
    Similar dynamic knee stability but different movement strategies and between-leg asymmetries for hip and knee joints for ACL-reconstructed persons relative to knee-healthy controls2018In: 8th World Congress of Biomechanics, Dublin, July 8-12, 2018, 2018Conference paper (Refereed)
  • 11.
    Markström, Jonas
    et al.
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Grip, Helena
    Umeå University, Faculty of Medicine, Department of Radiation Sciences.
    Schelin, Lina
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Häger, Charlotte K.
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Dynamic knee control and movement strategies in athletes and non‐athletes in side hops: implications for knee injury2019In: Scandinavian Journal of Medicine and Science in Sports, ISSN 0905-7188, E-ISSN 1600-0838, Vol. 29, no 8, p. 1181-1189Article in journal (Refereed)
    Abstract [en]

    Athletes exposed to rapid maneuvers need a high level of dynamic knee stability and robustness, while also controlling whole body movement, to decrease the risk of non‐contact knee injury. The effects of high‐level athletic training on such measures of movement control have not, however, been thoroughly evaluated. This study investigated whether elite athletes (who regularly perform knee‐specific neuromuscular training) show greater dynamic knee robustness and/or different movement strategies than non‐athletic controls, in relation to overall knee function. Thirty‐nine women (19 athletes, 20 controls) performed standardized rebound side hops (SRSH) while a motion capture system synchronized with two force plates registered three‐dimensional trunk, hip, and knee joint angles and moments. Dynamic knee robustness was evaluated using finite helical axis (FHA) inclination angles extracted from knee rotation intervals of 10°, analyzed with independent t tests. Angle and moment curves were analyzed with inferential methods for functional data. Athletes had superior knee function (less laxity, greater hop performances, and strength) but presented similar FHA inclination angles to controls. Movement strategies during the landing phase differed; athletes presented larger (a) hip flexion angles (during 9%‐29% of the phase), (b) hip adduction moments (59%‐99%), (c) hip internal rotation moments (83%‐89%), and (d) knee flexion moments (79%‐93%). Thus, elite athletes may have a greater ability than non‐athletes to keep the knee robust while performing SRSH more efficiently through increased engagement of the hip. However, dynamic knee robustness associated with lower FHA inclination angles still show room for improvement, thus possibly decreasing knee injury risk.

  • 12.
    Markström, Jonas L.
    et al.
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Grip, Helena
    Umeå University, Faculty of Medicine, Department of Radiation Sciences.
    Schelin, Lina
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Häger, Charlotte K.
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Individuals with anterior cruciate ligament reconstruction adopt different movement strategies but display robust knees during side hop landingsManuscript (preprint) (Other academic)
  • 13.
    Markström, Jonas L.
    et al.
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Schelin, Lina
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Häger, Charlotte K.
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    A novel standardised side hop test reliably evaluates landing mechanics for anterior cruciate ligament reconstructed persons and controls2018In: Sports Biomechanics, ISSN 1476-3141, E-ISSN 1752-6116Article in journal (Refereed)
    Abstract [en]

    We propose a novel one-leg standardised rebound side-hop test (SRSH) specifically designed for detailed analysis of landing mechanics. Anterior cruciate ligament reconstructed persons (ACLR, n = 30) and healthy-knee controls (CTRL, n = 30) were tested for within-session and test-retest (CTRL only, n = 25) reliability and agreement. Trunk, hip and knee angles and moments in sagittal, frontal, and transversal planes during landing, including time to stabilisation (TTS), were evaluated using intra-class correlations (ICCs), average within-person standard deviations (SW) and minimal differences. Excellent within-session reliability were found for angles in both groups (most ICCs > 0.90, SW ≤ 5°), and excellent to good for moments (most ICCs > 0.80, SW ≤ 0.34 Nm/kg). Only knee internal rotation moment showed poor reliability (ICC < 0.4). Test-retest results were excellent to fair for all angles and moments (ICCs 0.47–0.91, SW < 5° and ≤ 0.25 Nm/kg), except for peak trunk lateral bending angle and knee internal rotation moment. TTS showed excellent to fair within-session reliability but poor test-retest results. These results, with a few exceptions, suggest promising potential of evaluating landing mechanics during the SRSH for ACLR and CTRL, and emphasise the importance of joint-specific movement control variables in standardised tasks.

  • 14.
    Markström, Jonas L.
    et al.
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Tengman, Eva
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Grip, Helena
    Umeå University, Faculty of Medicine, Department of Radiation Sciences.
    Schelin, Lina
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Häger, Charlotte K.
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    A comparison of knee joint kinematics and kinetics during landings in three one-leg hop tests (hop for distance, vertical hop and side hop) performed by female elite floorball athletes2016In: XXI ISEK Congress: Bridges to Innovation, 2016Conference paper (Refereed)
  • 15.
    Pini, Alessia
    et al.
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Markström, Jonas
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation.
    Schelin, Lina
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Test-retest reliability measures for curve data: an overview with recommendations and supplementary code.2019In: Sports Biomechanics, ISSN 1476-3141, E-ISSN 1752-6116, p. 1-22Article in journal (Refereed)
    Abstract [en]

    The purpose of this paper is to provide an overview of available methods for reliability investigations when the outcome of interest is a curve. Curve data, or functional data, is commonly collected in biomechanical research in order to better understand different aspects of human movement. Using recent statistical developments, curve data can be analysed in its most detailed form, as functions. However, an overview of appropriate statistical methods for assessing reliability of curve data is lacking. A review of contemporary literature of reliability measures for curve data within the fields of biomechanics and statistics identified the following methods: coefficient of multiple correlation, functional limits of agreement, measures of distance and similarity, and integrated pointwise indices (an extension of univariate reliability measures to curve data, inclusive of Pearson correlation, intraclass correlation, and standard error of measurement). These methods are briefly presented, implemented (R-code available as supplementary material) and evaluated on simulated data to highlight advantages and disadvantages of the methods. Among the identified methods, the integrated intraclass correlation and standard error of measurement are recommended. These methods are straightforward to implement, enable results over the domain, and consider variation between individuals, which the other methods partly neglect.

  • 16.
    Schelin, Lina
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Spatial sampling and prediction2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis discusses two aspects of spatial statistics: sampling and prediction. In spatial statistics, we observe some phenomena in space. Space is typically of two or three dimensions, but can be of higher dimension. Questions in mind could be; What is the total amount of gold in a gold-mine? How much precipitation could we expect in a specific unobserved location? What is the total tree volume in a forest area? In spatial sampling the aim is to estimate global quantities, such as population totals, based on samples of locations (papers III and IV). In spatial prediction the aim is to estimate local quantities, such as the value at a single unobserved location, with a measure of uncertainty (papers I, II and V).

    In papers III and IV, we propose sampling designs for selecting representative probability samples in presence of auxiliary variables. If the phenomena under study have clear trends in the auxiliary space, estimation of population quantities can be improved by using representative samples. Such samples also enable estimation of population quantities in subspaces and are especially needed for multi-purpose surveys, when several target variables are of interest.

    In papers I and II, the objective is to construct valid prediction intervals for the value at a new location, given observed data. Prediction intervals typically rely on the kriging predictor having a Gaussian distribution. In paper I, we show that the distribution of the kriging predictor can be far from Gaussian, even asymptotically. This motivated us to propose a semiparametric method that does not require distributional assumptions. Prediction intervals are constructed from the plug-in ordinary kriging predictor. In paper V, we consider prediction in the presence of left-censoring, where observations falling below a minimum detection limit are not fully recorded. We review existing methods and propose a semi-naive method. The semi-naive method is compared to one model-based method and two naive methods, all based on variants of the kriging predictor.

  • 17.
    Schelin, Lina
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Sjöstedt-de Luna, Sara
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Construction of kriging prediction intervals for non-Gaussian spatial processesManuscript (preprint) (Other academic)
    Abstract [en]

    In this article, we compare three methods to construct prediction intervals for the value of a stationary process, based on plug-in ordinary kriging predictors. Ordinary kriging is a widely used method for prediction that, given observations of a (spatial) process, forms the best linear unbiased predictor of the process at a new location. Construction of prediction intervals for the value of interest based on ordinary kriging predictors typically rely on Gaussian assumptions. Special attention is here given to non-Gaussian processes, where construction of such intervals is less straightforward.  Methods based on asymptotic normality, Gaussian transformations and semiparametric bootstrap are compared on simulated and real data. The study suggests that the semiparametric method (that does not rely on distributional assumptions) is robust and is to be recommended for non-Gaussian processes. For practitioners the semiparametric method is an attractive alternative since the method can be used without spcifying a link function or making distributional assumptions.

  • 18.
    Schelin, Lina
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Sjöstedt-de Luna, Sara
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Kriging prediction intervals based on semiparametric bootstrap2010In: Mathematical Geosciences, ISSN 1874-8961, E-ISSN 1874-8953, Vol. 42, no 8, p. 985-1000Article in journal (Refereed)
    Abstract [en]

    Kriging is a widely used method for prediction, which, given observations of a (spatial) process, yields the best linear unbiased predictor of the process at a new location. The construction of corresponding prediction intervals typically relies on Gaussian assumptions. Here we show that the distribution of kriging predictors for non-Gaussian processes may be far from Gaussian, even asymptotically. This emphasizes the need for other ways to construct prediction intervals. We propose a semiparametric bootstrap method with focus on the ordinary kriging predictor. No distributional assumptions about the data generating process are needed. A simulation study for Gaussian as well as lognormal processes shows that the semiparametric bootstrap method works well. For the lognormal process we see significant improvement in coverage probability compared to traditional methods relying on Gaussian assumptions.

  • 19.
    Schelin, Lina
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Sjöstedt-de Luna, Sara
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Spatial prediction in the presence of left-censoring2014In: Computational Statistics & Data Analysis, ISSN 0167-9473, E-ISSN 1872-7352, Vol. 74, p. 125-141Article in journal (Other academic)
    Abstract [en]

    Environmental (spatial) monitoring of different variables often involves left-censored observations falling below the minimum detection limit (MDL) of the instruments used to quantify them. Several methods to predict the variables at new locations given left-censored observations of a stationary spatial process are compared. The methods use versions of kriging predictors, being the best linear unbiased predictors minimizing the mean squared prediction errors. A semi-naive method that determines imputed values at censored locations in an iterative algorithm together with variogram estimation is proposed. It is compared with a computationally intensive method relying on Gaussian assumptions, as well as with two distribution-free methods that impute the MDL or MDL divided by two at the locations with censored values. Their predictive performance is compared in a simulation study for both Gaussian and non-Gaussian processes and discussed in relation to the complexity of the methods from a user’s perspective. The method relying on Gaussian assumptions performs, as expected, best not only for Gaussian processes, but also for other processes with symmetric marginal distributions. Some of the (semi-)naive methods also work well for these cases. For processes with skewed marginal distributions (semi-)naive methods work better. The main differences in predictive performance arise for small true values. For large true values no difference between methods is apparent.

  • 20.
    Schelin, Lina
    et al.
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics. Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Tengman, Eva
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Ryden, Patrik
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Häger, Charlotte
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    A statistically compiled test battery for feasible evaluation of knee function after rupture of the Anterior Cruciate Ligament - derived from long-term follow-up data.2017In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 12, no 5, article id e0176247Article in journal (Refereed)
    Abstract [en]

    PURPOSE: Clinical test batteries for evaluation of knee function after injury to the Anterior Cruciate Ligament (ACL) should be valid and feasible, while reliably capturing the outcome of rehabilitation. There is currently a lack of consensus as to which of the many available assessment tools for knee function that should be included. The present aim was to use a statistical approach to investigate the contribution of frequently used tests to avoid redundancy, and filter them down to a proposed comprehensive and yet feasible test battery for long-term evaluation after ACL injury.

    METHODS: In total 48 outcome variables related to knee function, all potentially relevant for a long-term follow-up, were included from a cross-sectional study where 70 ACL-injured (17-28 years post injury) individuals were compared to 33 controls. Cluster analysis and logistic regression were used to group variables and identify an optimal test battery, from which a summarized estimator of knee function representing various functional aspects was derived.

    RESULTS: As expected, several variables were strongly correlated, and the variables also fell into logical clusters with higher within-correlation (max ρ = 0.61) than between clusters (max ρ = 0.19). An extracted test battery with just four variables assessing one-leg balance, isokinetic knee extension strength and hop performance (one-leg hop, side hop) were mathematically combined to an estimator of knee function, which acceptably classified ACL-injured individuals and controls. This estimator, derived from objective measures, correlated significantly with self-reported function, e.g. Lysholm score (ρ = 0.66; p<0.001).

    CONCLUSIONS: The proposed test battery, based on a solid statistical approach, includes assessments which are all clinically feasible, while also covering complementary aspects of knee function. Similar test batteries could be determined for earlier phases of ACL rehabilitation or to enable longitudinal monitoring. Such developments, established on a well-grounded consensus of measurements, would facilitate comparisons of studies and enable evidence-based rehabilitation.

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