A leap into functional Hilbert spaces with Harold Hotelling

Alessia Pini, A. Stamm, S. Vantini

Risultato della ricerca: Contributo in libroContributo a convegno

Abstract

The talk will focus on 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 will present a definition of Hotelling’s T2 statistic that naturally expands to any separable Hilbert space. In detail, we will present a unified framework for making inference on the mean element of Hilbert populations based on Hotelling’s T2 statistic, using a permutation-based testing procedure. We will then present the theoretical properties of the procedure (i.e., finitesample exactness and consistency) and show the explicit form of Hotelling’s T2 statistic in the case of some famous spaces used in functional data analysis like Sobolev and Bayes spaces.
Lingua originaleEnglish
Titolo della pubblicazione ospiteCladag 2017 Meeting of the Classification and Data Analysis Group Book of Short Papers
Pagine1-4
Numero di pagine4
Stato di pubblicazionePubblicato - 2017
EventoCladag 2017 Meeting of the Classification and Data Analysis Group Book - Milano
Durata: 13 set 201715 set 2017

Convegno

ConvegnoCladag 2017 Meeting of the Classification and Data Analysis Group Book
CittàMilano
Periodo13/9/1715/9/17

Keywords

  • functional data analysis, object-oriented data analysis, null hypothesis testing

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