| Issue |
ESAIM: PS
Volume 23, 2019
|
|
|---|---|---|
| Page(s) | 672 - 696 | |
| DOI | https://doi.org/10.1051/ps/2019020 | |
| Published online | 26 September 2019 | |
A test for block circular symmetric covariance structure with divergent dimension*
School of Mathematics and Statistics, Henan University,
Kaifeng
475000, PR China.
** Corresponding author: xjsnwpu@163.com
Received:
11
August
2018
Accepted:
2
September
2019
The paper considers the likelihood ratio (LR) test on the block circular symmetric covariance structure of a multivariate Gaussian population with divergent dimension. When the sample size n, the dimension of each block p and the number of blocks u satisfy pu < n − 1 and p = p(n) → ∞ as n → ∞, the asymptotic distribution and the moderate deviation principle of the logarithmic LR test statistic under the null hypothesis are established. Some numerical simulations indicate that the proposed LR test method performs well in the divergent-dimensional block circular symmetric covariance structure test.
Mathematics Subject Classification: 62H15 / 62E20
Key words: Likelihood ratio test / block circular symmetric model / asymptotic normality / moderate deviation principle
© EDP Sciences, SMAI 2019
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