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.

Hotelling in wonderland

A. Pini;A. Stamm;S. Vantini
2017-01-01

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.
2017
Functional Statistics and Related Fields
978-3-319-55845-5
File in questo prodotto:
File Dimensione Formato  
Pini_etal_IWFOS2017_Hotelling.pdf

Accesso riservato

: Publisher’s version
Dimensione 215.55 kB
Formato Adobe PDF
215.55 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1036000
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 2
social impact