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摘要暂缺

协方差矩阵特征根联合与边际分布的渐近展开AI 解读

Let nS be an $m\times m$ matrix having the Wishart distribution $W_m(n,\Sigma)$. For large n and simple latent roots of $\Sigma$, it is known that the latent roots of S are asymptotically independently normal. In this paper an expansion, up to and including the terms of order $n^-1$, is given for the joint density function of the roots of S in terms of normal density functions. Expansions for the marginal distributions of the roots are also given, valid when the…

摘要暂缺

样本协方差矩阵极端特征根分布函数的界AI 解读

An upper bound is given for the distribution function of the largest latent root and a lower bound for the distribution function of the smallest latent root for a sample covariance matrix from a normal population. The bounds are expressed in terms of products of chi-squared probabilities.