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.
Accepté le :
DOI : 10.1051/ps/2019020
Mots-clés : Likelihood ratio test, block circular symmetric model, asymptotic normality, moderate deviation principle
@article{PS_2019__23__672_0,
author = {Xie, Junshan and Sun, Gaoming},
title = {A test for block circular symmetric covariance structure with divergent dimension},
journal = {ESAIM: Probability and Statistics},
pages = {672--696},
publisher = {EDP-Sciences},
volume = {23},
year = {2019},
doi = {10.1051/ps/2019020},
mrnumber = {4011570},
zbl = {1507.62255},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2019020/}
}
TY - JOUR AU - Xie, Junshan AU - Sun, Gaoming TI - A test for block circular symmetric covariance structure with divergent dimension JO - ESAIM: Probability and Statistics PY - 2019 SP - 672 EP - 696 VL - 23 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2019020/ DO - 10.1051/ps/2019020 LA - en ID - PS_2019__23__672_0 ER -
%0 Journal Article %A Xie, Junshan %A Sun, Gaoming %T A test for block circular symmetric covariance structure with divergent dimension %J ESAIM: Probability and Statistics %D 2019 %P 672-696 %V 23 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2019020/ %R 10.1051/ps/2019020 %G en %F PS_2019__23__672_0
Xie, Junshan; Sun, Gaoming. A test for block circular symmetric covariance structure with divergent dimension. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 672-696. doi : 10.1051/ps/2019020. http://www.numdam.org/articles/10.1051/ps/2019020/
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