Hotelling in Wonderland

Alessia Pini, Aymeric Stamm, Simone Vantini

Risultato della ricerca: Contributo in libroChapter

Abstract

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.
Lingua originaleEnglish
Titolo della pubblicazione ospiteFunctional Statistics and Related Fields
EditorG. Aneiros, E. Bongiorno, R. Cao, P. Vieu
Pagine211-216
Numero di pagine6
DOI
Stato di pubblicazionePubblicato - 2017

Keywords

  • Hotelling's T-square
  • Nonparametric inference
  • functional data analysis

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