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家族数据中多元类间与类内相关指标的推断AI 解读

SUMMARY Multivariate measures of interclass and intraclass correlations are introduced to assess the degree of resemblance between family members with respect to more than one characteristic. Unified estimators for the multivariate measures are proposed as the eigenvalues of certain random matrices constructed by the matrices of the weighted sums of squares and products of observations. Asymptotic distributions of the proposed estimators are derived under the assumption of…

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关于二次型服从卡方分布的充要条件的一则说明AI 解读

Necessary and sufficient conditions for a quadratic form to be chi-squared given by Khatri (1963), Shanbhag (1968) and Good (1969, 1970) are compared. Some remarks on these results are made.

方向统计中的 von Mises–Fisher 矩阵分布AI 解读

Summary When n distinguishable directions in p dimensions are required to describe each orientation, Downs (1972) has extended the von Mises–Fisher distribution. We obtain the normalizing constant which leads to the investigation of various basic properties of the distribution. In particular, an explicit expression for the first population moment as well as the asymptotic distribution of the basic statistics are provided. The estimation problem, important testing problems,…

不完全区组设计中区组间与区组内合并估计的精确方差AI 解读

This article presents methods for evaluating exact variance of combined inter- and intra-block estimates of treatment effects in incomplete block designs. The results are valid for all incomplete block designs and hold for a wide class of combined estimates including most in the literature. Tables of exact variance for some estimates are presented for some balanced designs and for some partially balanced designs.

不完全区组设计中区组间与区组内组合估计的精确方差AI 解读

This article presents methods for evaluating exact variance of combined inter- and intra-block estimates of treatment effects in incomplete block designs. The results are valid for all incomplete block designs and hold for a wide class of combined estimates including most in the literature. Tables of exact variance for some estimates are presented for some balanced designs and for some partially balanced designs.

非中心 Wishart 矩阵初等对称函数期望猜想的证明AI 解读

This paper provides proof of conjectures about the expected values of the $j$th elementary symmetric function of the roots (i.e. $E(\operatorname{tr}_j A)$) of a non-central Wishart matrix. Utilizing this result we have obtained computationally convenient formula for the expected value of the $j$th elementary symmetric function of the roots of central positive definite quadratic form in matrix argument.

协方差矩阵似然比检验在非零假设下的分布渐近展开AI 解读

In this paper, asymptotic expansions of the non-null distributions of the likelihood ratio criteria are obtained for testing the hypotheses: (a) $H_1: \Sigma = \sigma^2I, \sigma^2 > 0$, (b) $H_2: \Sigma_1 = \Sigma_2$, against alternatives which are close to the hypothesis. These expansions are of chi-square type. The first problem has been considered by Sugiura (1969) but because of the singularity at the hypothesis, his expansion will not be good for alternatives close to…

多元线性回归中最小二乘的一个定理AI 解读

This note shows that the least squares estimate of the matrix of coefficients in multivariate linear regression model maximizes all the sample canonical correlations between the dependent variables and the linear transformations of the explanatory variables, and it maximizes all the characteristic roots of the sample regression sum of squares and products matrix due to regression of the dependent variables on the linear transformations of the explanatory variables.

关于多元线性回归最小二乘法的一个定理AI 解读

This note shows that the least squares estimate of the matrix of coefficients in multivariate linear regression model maximizes all the sample canonical correlations between the dependent variables and the linear transformations of the explanatory variables, and it maximizes all the characteristic roots of the sample regression sum of squares and products matrix due to regression of the dependent variables on the linear transformations of the explanatory variables.

截断二元正态分布的参数估计AI 解读

Estimates of parameters of a singly truncated bivariate normal distribution have been directly obtained using eight (or nine) moments. Asymptotic variances and covariances of these estimates are given and they are compared with those of maximum likelihood estimates.

单侧截断二元正态分布的参数估计AI 解读

Estimates of parameters of a singly truncated bivariate normal distribution have been directly obtained using eight (or nine) moments. Asymptotic variances and covariances of these estimates are given and they are compared with those of maximum likelihood estimates.