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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.
    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.

  • 2.
    Cremona, Marzia Angela
    et al.
    Penn State University.
    Rebeca, Campos Sánchez
    Penn State University.
    Pini, Alessia
    Politecnico di Milano.
    Vantini, Simone
    Politecnico di Milano.
    Katerina, Makova
    Penn State University.
    Francesca, Chiaromonte
    Penn State University.
    Functional data analysis of "Omics" data: how does the genomic landscape influence integration and fixation of endogenous retroviruses?2017In: Functional statistics and related fields / [ed] Germán Aneiros, Enea G. Bongiorno, Ricardo Cao, Philippe Vieu, Springer, 2017, p. 87-93Chapter in book (Refereed)
    Abstract [en]

     We consider thousands of endogenous retrovirus detected in the human and mouse genomes, and quantify a large number of genomic landscape features at high resolution around their integration sites and in control regions. We propose to analyze this data employing a recently developed functional inferential procedure and functional logistic regression, with the aim of gaining insights on the effects of genomic landscape features on the integration and fixation of endogenous retroviruses.

  • 3.
    Pini, Alessia
    et al.
    MOX - Department of Mathematics, Politecnico di Milano, Milano, Italy.
    Lorenzo, Spreafico
    Simone, Vantini
    Alessandro, Vietti
    Differential interval-wise testing for local inference in Sobolev spaces2017In: Functional statistics and related fields / [ed] Germán Aneiros, Enea G. Bongiorno, Ricardo Cao, Philippe Vieu, Springer, 2017, p. 203-210Chapter in book (Refereed)
    Abstract [en]

    We present a local non-parametric inferential technique - namely, the differential interval-wise testing, or D-IWT - able to test the distributional equality of two samples of functional data embedded in Sobolev spaces. D-IWT can impute differences between the two samples to specific parts of the domain and to specific orders of differentiation. The proposed technique is applied to the functional data analysis of a data set of tongue profiles.

  • 4.
    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.

  • 5.
    Pini, Alessia
    et al.
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Spreafico, Lorenzo
    Vantini, Simone
    Vietti, Alessandro
    Multi-aspect local inference for functional data: Analysis of ultrasound tongue profiles2019In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 170, p. 162-185Article in journal (Refereed)
    Abstract [en]

    Motivated by the analysis of a dataset of ultrasound tongue profiles, we present multi-aspect interval-wise testing (IWT), i.e., a local nonparametric inferential technique for functional data embedded in Sobolev spaces. Multi-aspect IWT is a nonparametric procedure that tests differences between groups of functional data, jointly taking into account the curves and their derivatives. Multi-aspect IWT provides adjusted multi-aspect p-value functions that can be used to select intervals of the domain that are imputable for the rejection of a null hypothesis. As a result, it can impute the rejection of a functional null hypothesis to specific intervals of the domain and to specific orders of differentiation. We show that the multi-aspect p-value functions are provided with a control of the family wise error rate and that they are consistent. We apply multi-aspect IWT to the analysis of a dataset of tongue profiles recorded for a study on Tyrolean, a German dialect spoken in South Tyrol. We test differences between five different ways of articulating the uvular /r/: vocalized /r/, approximant, fricative, tap, and trill. Multi-aspect IWT-based comparisons result in an informative and detailed representation of the regions of the tongue where a significant difference occurs. 

  • 6.
    Pini, Alessia
    et al.
    Politecnico di Milano.
    Stamm, Aymeric
    Politecnico di Milano.
    Vantini, Simone
    Politecnico di Milano.
    Hotelling in wonderland2017In: Functional statistics and related fields / [ed] Germán Aneiros, Enea G. Bongiorno, Ricardo Cao, Philippe Vieu, Springer, 2017, p. 221-216Chapter in book (Refereed)
    Abstract [en]

     While Hotelling's T2 statistic is traditionally defined as the Mahalanobis distance between the sample mean and the true mean induced by the inverse of the sample covariance matrix, we hereby propose an alternative definition which allows a unifying and coherent definition of Hotelling's T2 statistic in any Hilbert space independently from its dimensionality and sample size. In details, we introduce the definition of random variables in Hilbert spaces, the concept of mean and covariance in such spaces and the relevant operators for formulating a proper definition of Hotelling's T2  statistic relying on the concept of Bochner integral.

  • 7.
    Pini, Alessia
    et al.
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics. MOX - Dept. of Mathematics, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133 Milano, Italy; Department of Statistical Sciences, Università Cattolica del Sacro Cuore, Largo A. Gemelli 1, 20123 Milano, Italy.
    Stamm, Aymeric
    Vantini, Simone
    Hotelling's T-2 in separable Hilbert spaces2018In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 167, p. 284-305Article in journal (Refereed)
    Abstract [en]

    We address the problem of finite-sample null hypothesis significance testing on the mean element of a random variable that takes value in a generic separable Hilbert space. For this purpose, we propose a (re)definition of Hotelling's T-2 that naturally expands to any separable Hilbert space that we further embed within a permutation inferential approach. In detail, we present a unified framework for making inference on the mean element of Hilbert populations based on Hotelling's T-2 statistic, using a permutation-based testing procedure of which we prove finite-sample exactness and consistency; we showcase the explicit form of Hotelling's T-2 statistic in the case of some famous spaces used in functional data analysis (i.e., Sobolev and Bayes spaces); we demonstrate, by means of simulations, that Hotelling's T-2 exhibits the best performances in terms of statistical power for detecting mean differences between Gaussian populations, compared to other state-of-the-art statistics, in most simulated scenarios; we propose a case study that demonstrate the importance of the space into which one decides to embed the data; we provide an implementation of the proposed tools in the R package fdahotelling available at https://github.com/astamm/fdahotelling. 

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