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多线性主成分分析中 Kronecker 包络模型的检验AI 解读

We develop likelihood methods for the Kronecker envelope model in the principal components analysis of matrix observations that have a multivariate normal distribution. Maximum likelihood estimates are derived and the associated likelihood ratio statistic for a test of this Knonecker envelope model is obtained. The asymptotic null distribution of the likelihood ratio statistic is derived as some nuisance parameters approach infinity, and a saddlepoint approximation for this…

多元线性回归包络模型的似然比检验AI 解读

We investigate the likelihood ratio test for a hypothesis regarding the dimension of the Σ-envelope of span(β) in a multivariate linear regression model. The asymptotic null distribution of the likelihood ratio statistic is obtained as some nuisance parameters approach infinity. A saddlepoint approximation is also given for this limiting distribution. The accuracy of this approximation and its comparison to the standard chi-squared approximation are assessed via simulation.…

部分共同主成分子空间的加权卡方检验AI 解读

We consider tests of the null hypothesis that g covariance matrices have a partial common principal component subspace of dimension s. Our approach uses a dimensionality matrix which has its rank equal to s when the hypothesis holds. The test can then be based on a statistic computed from the eigenvalues of an estimate of this dimensionality matrix. The asymptotic distribution of this statistic is that of a linear combination of independent one‐degree‐of‐freedom chi‐squared…