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 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

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

Bibliographic databases:

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
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