An Asymptotic Two-Sided Test in a Family of Multivariate Distribution

DOI

10.2991/jsta.d.200511.001How to use a DOI?

Keywords

Asymptotic two-sided test; Chi-squared distribution; Efficient algorithm; Multivariate distribution elements

Abstract

In the present paper, a two-sided test in a family of multivariate distribution according to the Mahalanobis distance with mean vector and positive definite matrix is considered. First, a family of multivariate distribution is introduced, then using the likelihood ratio method a test statistic is computed. The distribution of the test statistic is proposed for different sample sizes and fixed dimension. We study the distribution approximation computed using the likelihood ratio test and an efficient algorithm to compute the density functions can be derived according to Witkovsk´y, J. Stat. Plan. Inference. 94 (2001), 1–13. Also, a simulation study is presented on the sample sizes and powers to compare the performance of tests and show that the proposed distribution approximation is better than the classical distribution approximation.

Copyright

© 2020 The Authors. Published by Atlantis Press SARL.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Abouzar Bazyari
AU  - Mahmoud Afshari
AU  - Monjed H. Samuh
PY  - 2020
DA  - 2020/05/26
TI  - An Asymptotic Two-Sided Test in a Family of Multivariate Distribution
JO  - Journal of Statistical Theory and Applications
SP  - 162
EP  - 172
VL  - 19
IS  - 2
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.200511.001
DO  - 10.2991/jsta.d.200511.001
ID  - Bazyari2020
ER  -