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- W3204253344 abstract "Consider $k$ independent random samples from $p$-dimensional multivariate normal distributions. We are interested in the limiting distribution of the log-likelihood ratio test statistics for testing for the equality of $k$ covariance matrices. It is well known from classical multivariate statistics that the limit is a chi-square distribution when $k$ and $p$ are fixed integers. Jiang and Yang~cite{JY13} and Jiang and Qi~cite{JQ15} have obtained the central limit theorem for the log-likelihood ratio test statistics when the dimensionality $p$ goes to infinity with the sample sizes. In this paper, we derive the central limit theorem when either $p$ or $k$ goes to infinity. We also propose adjusted test statistics which can be well approximated by chi-squared distributions regardless of values for $p$ and $k$. Furthermore, we present numerical simulation results to evaluate the performance of our adjusted test statistics and the log-likelihood ratio statistics based on classical chi-square approximation and the normal approximation." @default.
- W3204253344 created "2021-10-11" @default.
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- W3204253344 date "2021-10-05" @default.
- W3204253344 modified "2023-10-17" @default.
- W3204253344 title "Asymptotic Distributions for Likelihood Ratio Tests for the Equality of Covariance Matrices" @default.
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- W3204253344 doi "https://doi.org/10.48550/arxiv.2110.02384" @default.
- W3204253344 hasPublicationYear "2021" @default.
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