论文检索

多元方差分析与典型相关分析中的参数矩阵及特征值估计AI 解读

We consider the problem of estimating parameter matrices which occur in the noncentral Wishart, noncentral multivariate $F$ and canonical correlations distributions. A decision-theoretic approach is taken with squared error as the loss function. In these three settings the eigenvalues of the parameter matrices are of primary interest. Sensible estimates of these are obtained by restricting attention to orthogonally invariant estimates of the parameter matrices, whose…

复相关系数某一特定函数的估计AI 解读

Let R denote the sample multiple correlation coefficient formed from a sample from a normal distribution with population multiple correlation coefficient . This article considers the problem of estimating the parameter using quadratic loss. The best unbiased estimate of θ is a linear function of Y = R 2/(1 − R 2); it is shown that this is dominated by other linear estimates and that these, in turn, are dominated by nonlinear estimates. A Monte Carlo study indicates that such…

摘要暂缺

非正态总体下典型相关分析及其他多元方法的渐近分布AI 解读

An asymptotic theory for canonical correlation analysis is given for multivariate populations with finite fourth moments. The asymptotic distributions of the sample canonical correlation coefficients and of statistics used for testing hypotheses about the population coefficients involve the fourth order cumulants of the parent population and are sensitive to departures from normality. These asymptotic distributions have surprisingly simple forms in the case of elliptical…

非正态总体下典型相关分析及其他多元方法的渐近分布AI 解读

An asymptotic theory for canonical correlation analysis is given for multivariate populations with finite fourth moments. The asymptotic distributions of the sample canonical correlation coefficients and of statistics used for testing hypotheses about the population coefficients involve the fourth order cumulants of the parent population and are sensitive to departures from normality. These asymptotic distributions have surprisingly simple forms in the case of elliptical…

特征根与矩阵随机变量：若干渐近结果综述AI 解读

The exact noncentral distributions of matrix variates and latent roots derived from normal samples involve hypergeometric functions of matrix argument. These functions can be defined as power series, by integral representations, or as solutions of differential equations, and there is no doubt that these mathematical characterizations have been a unifying influence in multivariate noncentral distribution theory, at least from an analytic point of view. From a computational…