Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teor. Veroyatnost. i Primenen., 2019, Volume 64, Issue 2, Pages 358–374 (Mi tvp5224)  

Testing a multivariate distribution for generalized skew ellipticity

L. A. Sakhanenko

Department of Statistics and Probability, Michigan State University, East Lansing, MI, USA

Abstract: We consider the problem of testing whether a sample comes from a family of the multivariate generalized skew-elliptical distributions with an unknown location parameter, an unknown scaling matrix, and an unknown distribution of the symmetric component, specified up to a parameter skewing function with an unknown parameter value. We propose test statistics that are functionals of empirical processes indexed by classes of functions. Under mild smoothness conditions on the skewing function and the functional class, we obtain the asymptotic theory for these tests. They are consistent against any fixed alternative, invariant under a group of affine transformations, and flexible to implement. However, the limiting process depends on the unknown parameters in a complicated way. To overcome this obstacle, we propose a bootstrapped modification of the testing procedure, prove that it works theoretically, and illustrate its practical performance on a simulation study.

Keywords: generalized skew-elliptical distribution, bootstrap, hypothesis testing.

Funding Agency Grant Number
National Science Foundation DMS-1208238
This research was partially supported by NSF grant DMS-1208238 and partially supported by Michigan State University High Performance Computing Center through computational resources provided by the Institute for Cyber-Enabled Research.


DOI: https://doi.org/10.4213/tvp5224

Full text: PDF file (490 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Theory of Probability and its Applications, 2019, 64:2, 290–303

Bibliographic databases:

Received: 01.05.2017
Accepted:21.06.2018

Citation: L. A. Sakhanenko, “Testing a multivariate distribution for generalized skew ellipticity”, Teor. Veroyatnost. i Primenen., 64:2 (2019), 358–374; Theory Probab. Appl., 64:2 (2019), 290–303

Citation in format AMSBIB
\Bibitem{Sak19}
\by L.~A.~Sakhanenko
\paper Testing a~multivariate distribution for generalized skew ellipticity
\jour Teor. Veroyatnost. i Primenen.
\yr 2019
\vol 64
\issue 2
\pages 358--374
\mathnet{http://mi.mathnet.ru/tvp5224}
\crossref{https://doi.org/10.4213/tvp5224}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3943124}
\zmath{https://zbmath.org/?q=an:1426.62172}
\elib{https://elibrary.ru/item.asp?id=37298298}
\transl
\jour Theory Probab. Appl.
\yr 2019
\vol 64
\issue 2
\pages 290--303
\crossref{https://doi.org/10.1137/S0040585X97T989490}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000478971000007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85070989837}


Linking options:
  • http://mi.mathnet.ru/eng/tvp5224
  • https://doi.org/10.4213/tvp5224
  • http://mi.mathnet.ru/eng/tvp/v64/i2/p358

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:120
    References:17
    First page:8

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021