In estimation of a matrix of regressioncoefficients in a multivariate linear regression model. this paper shows that minimax and shrinkage estimators under a normal distribution remain robust under an elliptically co...
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In estimation of a matrix of regressioncoefficients in a multivariate linear regression model. this paper shows that minimax and shrinkage estimators under a normal distribution remain robust under an elliptically contoured distribution. The robustness of the improvement is established for both invariant and noninvariant loss functions in the above model as well as in the growth curve model. (C) 2001 Academic Press.
Consider a multivariate linear regression model where the sample size is n and the dimensions of the predictors and the responses are p and m, respectively. We know that the limiting distribution of the likelihood rat...
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Consider a multivariate linear regression model where the sample size is n and the dimensions of the predictors and the responses are p and m, respectively. We know that the limiting distribution of the likelihood ratio test (LRT) in multivariate linear regressions is different in the case of finite and high dimensions. In traditional multivariate analysis, when the dimension parameters (p, m) are fixed, the limiting distribution of the LRT is a chi 2 distribution. However, in the high-dimensional setting, the chi 2 approximation to the LRT may be invalid. In this paper, based on He et al. (2021), we give the moderate deviation principle (MDP) results for the LRT in a high dimensional setting, where the dimension parameters (p, m) are allowed to increase with the sample size n. The performance of the numerical simulation confirms our results. (c) 2022 Elsevier Inc. All rights reserved.
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