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多变量家庭数据的主成分分析AI 解读

The use of a principal component analysis is considered for multivariate data on families with different numbers of siblings. The coefficients in principal components are given as the eigenvectors of the weighted sums of squares and products matrix from the sibling data. Asymptotic distributions of the eigenvalues and eigenvectors of the estimated covariance matrix are obtained for an elliptical population. Asymptotic distributions of statistics associated with reduction of…

多元家庭数据的主成分分析AI 解读

The use of a principal component analysis is considered for multivariate data on families with different numbers of siblings. The coefficients in principal components are given as the eigenvectors of the weighted sums of squares and products matrix from the sibling data. Asymptotic distributions of the eigenvalues and eigenvectors of the estimated covariance matrix are obtained for an elliptical population. Asymptotic distributions of statistics associated with reduction of…

正态化变换与 Bootstrap 置信区间AI 解读

This paper considers the problem of constructing approximate confidence intervals for functional parameters in the nonparametric case. The approach based on transformation theory is applied to improve standard confidence intervals. The accelerated bias-corrected percentile interval introduced by Efron relies on the existence of a normalizing transformation with bias and skewness corrections, although calculation does not require explicit knowledge of its functional form. We…

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…

多元分析中若干统计量的正态化变换AI 解读

A general procedure for finding normalizing transformations is applied to various statistics in multivariate analysis. It is shown that Fisher's z transformation for a sample correlation coefficient in a normal sample and Wilson & Hilferty's approximation for a chi-squared variate can be derived by the same line of approach.

多元分析中若干统计量的正态化变换AI 解读

A general procedure for finding normalizing transformations is applied to various statistics in multivariate analysis. It is shown that Fisher's z transformation for a sample correlation coefficient in a normal sample and Wilson & Hilferty's approximation for a chi-squared variate can be derived by the same line of approach.

样本相关系数分布的一种近似AI 解读

A simple and accurate approximation to the distribution of the correlation coefficient in normal samples is obtained. The resulting approximation compares favourably with previous approximations.