Skip to main content

Research Repository

Advanced Search

Self–consistency–based tests for bivariate distributions

Einbeck, Jochen; Meintanis, Simos

Self–consistency–based tests for bivariate distributions Thumbnail


Authors

Simos Meintanis



Abstract

A novel family of tests based on the self–consistency property is developed. Our developments can be motivated by the well known fact that a two–dimensional spherically symmetric distribution X is self–consistent w.r.t. to the circle E||X||, that is, each point on that circle is the expectation of all observations that project onto that point. This fact allows the use of the self–consistency property in order to test for spherical symmetry. We construct an appropriate test statistic based on empirical characteristic functions, which turns out to have an appealing closed–form representation. Critical values of the test statistics are obtained empirically. The nominal level attainment of the test is verified in simulation, and the test power under several alternatives is studied. A similar test based on the self–consistency property is then also developed for the question of whether a given straight line corresponds to a principal component. The extendibility of this concept to further test problems for multivariate distributions is briefly discussed.

Citation

Einbeck, J., & Meintanis, S. (2017). Self–consistency–based tests for bivariate distributions. Journal of statistical theory and practice, 11(3), 478-492. https://doi.org/10.1080/15598608.2017.1318098

Journal Article Type Article
Acceptance Date Apr 7, 2017
Online Publication Date Apr 14, 2017
Publication Date Apr 14, 2017
Deposit Date Apr 25, 2017
Publicly Available Date Mar 29, 2024
Journal Journal of Statistical Theory and Practice
Electronic ISSN 1559-8616
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 11
Issue 3
Pages 478-492
DOI https://doi.org/10.1080/15598608.2017.1318098
Keywords Self-consistency, Empirical characteristic functions, Spherical symmetry, Principal curves, Principal components.

Files





You might also like



Downloadable Citations