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基于随机矩阵理论的高维多元方差分析特征值极限行为AI 解读

In this paper, we derive the asymptotic joint distributions of the eigenvalues under the null case and the local alternative cases in the MANOVA model and multiple discriminant analysis when both the dimension and the sample size are large. Our results are obtained by random matrix theory (RMT) without assuming normality in the populations. It is worth pointing out that the null and nonnull distributions of the eigenvalues and invariant test statistics are asymptotically…

高维主成分分析中 AIC 与 BIC 估计显著成分数的一致性AI 解读

In this paper, we study the problem of estimating the number of significant components in principal component analysis (PCA), which corresponds to the number of dominant eigenvalues of the covariance matrix of $p$ variables. Our purpose is to examine the consistency of the estimation criteria AIC and BIC based on the model selection criteria by Akaike [In 2nd International Symposium on Information Theory (1973) 267–281, Akadémia Kiado] and Schwarz [Estimating the dimension…

增长曲线模型中的协变量选择AI 解读

The growth curve model introduced by Potthoff & Roy (1964) is a generalization of the multivariate analysis of variance model and is often employed to analyze longitudinal data, in which a single characteristic has been measured at p different occasions on each individual. Inferential problems of this model are studied by using analysis of covariance, i.e. partitioning the p measurements into the measurements of q response variables and p-q covariables. Rao (1965, 1966) and…

增长曲线模型中的协变量选择AI 解读

The growth curve model introduced by Potthoff & Roy (1964) is a generalization of the multivariate analysis of variance model and is often employed to analyze longitudinal data, in which a single characteristic has been measured at p different occasions on each individual. Inferential problems of this model are studied by using analysis of covariance, i.e. partitioning the p measurements into the measurements of q response variables and p-q covariables. Rao (1965, 1966) and…

若干多元正态混合分布的渐近展开及误差界AI 解读

This paper deals with the distribution of $\mathbf{X} = \sum^{1/2}\mathbf{Z}$, where $\mathbf{Z}: p \times 1$ is distributed as $N_p(0, I_p), \sum$ is a positive definite random matrix and $\mathbf{Z}$ and $\sum$ are independent. Assuming that $\sum = I_p + BB'$, we obtain an asymptotic expansion of the distribution function of $\mathbf{X}$ and its error bound, which is useful in the situation where $\sum$ tends to $I_p$. A stronger version of the expansion is also given.…

多元线性模型估计量分布函数渐近展开的误差界AI 解读

In this paper we consider asymptotic approximations to the distribution function $F(x)$ of a linear combination of an estimate in a multivariate linear model. A method is given for obtaining an asymptotic expansion $F_{s - 1}(x)$ of $F(x)$ up to $O(n^{-s + 1})$ and a bound $c_s$ such that $|F(x) - F_{s - 1}(x)| \leq c_s$ uniformly in $x$ and $c_s = O(n^{-s})$.

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非正态总体下样本特征根分布的渐近展开AI 解读

The distribution of the latent roots of the sample covariance matrix is studied when the parent population is nonnormal. Asymptotic expansions of the marginal and joint distributions of the sample roots and the distribution of a function of the sample roots are given, by finding the Edgeworth expansions.

非正态总体下样本特征根分布的渐近展开AI 解读

The distribution of the latent roots of the sample covariance matrix is studied when the parent population is nonnormal. Asymptotic expansions of the marginal and joint distributions of the sample roots and the distribution of a function of the sample roots are given, by finding the Edgeworth expansions.