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  • 1.
    Abramowicz, Konrad
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Schelin, Lina
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Sjöstedt de Luna, Sara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Strandberg, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Multiresolution clustering of dependent functional data with application to climate reconstruction2019Ingår i: Stat, E-ISSN 2049-1573, Vol. 8, nr 1, artikel-id e240Artikel i tidskrift (Refereegranskat)
    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.

  • 2. Hébert-Losier, Kim
    et al.
    Pini, Alessia
    Vantini, Simone
    Strandberg, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Abramowicz, Konrad
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Schelin, Lina
    Umeå universitet, Medicinska fakulteten, Institutionen för samhällsmedicin och rehabilitering, Fysioterapi.
    Häger, Charlotte
    Umeå universitet, Medicinska fakulteten, Institutionen för samhällsmedicin och rehabilitering, Sjukgymnastik.
    One-leg hop kinematics 20years following anterior cruciate ligament rupture: Data revisited using functional data analysis2015Ingår i: Clinical Biomechanics, ISSN 0268-0033, E-ISSN 1879-1271, Vol. 30, nr 10, s. 1153-1161Artikel i tidskrift (Refereegranskat)
    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.

  • 3.
    Strandberg, Johan
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sjöstedt de Luna, Sara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Mateu, Jorge
    Prediction of spatial functional random processes: comparing functional and spatio-temporal kriging approaches2019Ingår i: Stochastic environmental research and risk assessment (Print), ISSN 1436-3240, E-ISSN 1436-3259, Vol. 33, nr 10, s. 1699-1719Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present and compare functional and spatio-temporal (Sp.T.) kriging approaches to predict spatial functional random processes (which can also be viewed as Sp.T. random processes). Comparisons with respect to computational time and prediction performance via functional cross-validation is evaluated, mainly through a simulation study but also on a real data set. We restrict comparisons to Sp.T. kriging versus ordinary kriging for functional data (OKFD), since the more flexible functional kriging approaches pointwise functional kriging (PWFK) and the functional kriging total model coincide with OKFD in several situations. Here we formulate conditions under which we show that OKFD and PWFK coincide. From the simulation study, it is concluded that the prediction performance of the two kriging approaches in general is rather equal for stationary Sp.T. processes. However, functional kriging tends to perform better for small sample sizes, while Sp.T. kriging works better for large sizes. For non-stationary Sp.T. processes, with a common deterministic time trend and/or time varying variances and dependence structure, OKFD performs better than Sp.T. kriging irrespective of the sample size. For all simulated cases, the computational time for OKFD was considerably lower compared to those for the Sp.T. kriging methods.

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