• Corpus ID: 238407892

Asymptotic Distributions for Likelihood Ratio Tests for the Equality of Covariance Matrices

@inproceedings{Guo2021AsymptoticDF,
  title={Asymptotic Distributions for Likelihood Ratio Tests for the Equality of Covariance Matrices},
  author={Wenchuan Guo and Yongcheng Qi},
  year={2021}
}

• Wenchuan Guo, Y. Qi
• Published 5 October 2021
• Mathematics

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 [12] and Jiang and Qi [11] have obtained the central limit theorem for the log-likelihood ratio test statistics when the dimension 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.