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Hotelling in wonderland
Politecnico di Milano.ORCID iD: 0000-0001-9235-3062
Politecnico di Milano.
Politecnico di Milano.
2017 (English)In: 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.

Place, publisher, year, edition, pages
Springer, 2017. p. 221-216
Series
Contributions to Statistics, ISSN 1431-1968
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:umu:diva-141354DOI: 10.1007/978-3-319-55846-2_28ISBN: 978-3-319-55846-2 (electronic)ISBN: 978-3-319-55845-5 (print)OAI: oai:DiVA.org:umu-141354DiVA, id: diva2:1153510
Note

Fourth International Workshop on Functional and Operatorial Statistics (IWFOS 2017), A Coruña, Spain, 15-17 June 2017.

Available from: 2017-10-30 Created: 2017-10-30 Last updated: 2018-06-09Bibliographically approved

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Pini, Alessia

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