Einbeck, Jochen and Meintanis, Simos (2017) 'Self–consistency–based tests for bivariate distributions.', Journal of statistical theory and practice., 11 (3). 478-492 .
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.
|Keywords:||Self-consistency, Empirical characteristic functions, Spherical symmetry, Principal curves, Principal components.|
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||https://doi.org/10.1080/15598608.2017.1318098|
|Publisher statement:||This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of Statistical Theory and Practice on 14/04/2017, available online at: http://www.tandfonline.com/10.1080/15598608.2017.1318098|
|Date accepted:||07 April 2017|
|Date deposited:||25 April 2017|
|Date of first online publication:||14 April 2017|
|Date first made open access:||14 April 2018|
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