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Hotelling's T-2 in separable Hilbert spaces
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.ORCID iD: 0000-0001-9235-3062
2018 (English)In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 167, p. 284-305Article in journal (Refereed) Published
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. 

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 167, p. 284-305
Keywords [en]
Hilbert space, functional data, high-dimensional data hotelling's T-2, nonparametric inference, rmutation test
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-151382DOI: 10.1016/j.jmva.2018.05.007ISI: 000441371100018OAI: oai:DiVA.org:umu-151382DiVA, id: diva2:1245943
Available from: 2018-09-06 Created: 2018-09-06 Last updated: 2018-09-06Bibliographically approved

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Pini, Alessia

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