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高维完全独立性检验AI 解读

A simple statistic is proposed for testing the complete independence of random variables having a multivariate normal distribution. The asymptotic null distribution of this statistic, as both the sample size and the number of variables go to infinity, is shown to be normal. Consequently, this test can be used when the number of variables is not small relative to the sample size and, in particular, even when the number of variables exceeds the sample size. The finite sample…

摘要暂缺

摘要暂缺

统计学中的矩阵分析AI 解读

Preface. 1. A Review of Elementary Matrix Algebra. 2. Vector Spaces. 3. Eigenvalues and Eigenvectors. 4. Matrix Factorizations and Martrix Norms. 5. Generalized Inverses. 6. Systems of Linear Equations. 7. Partitioned Matrices. 8. Special Matrices and Matrix Operations. 9. Matrix Derivatives and Related Topics. 10. Some Special Topics Related to Quadratic Forms. References. Index.

切片逆回归中的维数确定AI 解读

A general regression problem is one in which a response variable can be expressed as some function of one or more different linear combinations of a set of explanatory variables as well as a random error term. Sliced inverse regression is a method for determining these linear combinations. In this article we address the problem of determining how many linear combinations are involved. Procedures based on conditional means and conditional covariance matrices, as well as a…

多组共同主成分子空间的若干检验AI 解读

SUMMARY An approximate test, based on sample eigenprojections, is obtained for testing the hypothesis that the subspaces spanned by the first m principal components of several different covariance matrices are identical. This procedure can fairly easily be extended to an analogous test of hypothesis concerning correlation matrices. Extensions to a robust principal components analysis are also considered.

相关矩阵特定主成分的假设检验AI 解读

In the application of principal components analysis it is common to replace an observed sample principal component vector by another vector closely resembling the sample vector but which is easier to use or interpret. A useful test of hypothesis in this case is one that specifies the true ith principal component. In this article we obtain an asymptotically chi-squared procedure suitable for testing such a hypothesis when the principal components analysis is performed on a…

相关矩阵中特定主成分的检验AI 解读

In the application of principal components analysis it is common to replace an observed sample principal component vector by another vector closely resembling the sample vector but which is easier to use or interpret. A useful test of hypothesis in this case is one that specifies the true ith principal component. In this article we obtain an asymptotically chi-squared procedure suitable for testing such a hypothesis when the principal components analysis is performed on a…

多个群组共同主成分子空间的检验AI 解读

SUMMARY An approximate test, based on sample eigenprojections, is obtained for testing the hypothesis that the subspaces spanned by the first m principal components of several different covariance matrices are identical. This procedure can fairly easily be extended to an analogous test of hypothesis concerning correlation matrices. Extensions to a robust principal components analysis are also considered.

摘要暂缺

两组中的共同主成分子空间AI 解读

E. Keramidas has brought to my attention some related work by Keramidas, Devlin & Gnanadesikan (1987), who compared principal components of several covariance matrices by using a graphical procedure.

相关矩阵最小特征根相等性的检验AI 解读

The asymptotic variance of a statistic used to test the equality of the smallest latent roots of a correlation matrix is computed. This permits an approximation to its null distribution suggested by Lawley (1956). A simulation is used to compare the performance of this approximation with others currently in use.

两组数据的共同主成分子空间AI 解读

One important practical application of principal component analysis is to reduce a large number of variables, say p, to a smaller number, m, by making use of the first m principal components. This technique can easily be extended to two or more groups if the subspaces spanned by the first m principal components are the same for all groups. In this paper we develop an approximate procedure for testing such a hypothesis of common subspaces when two groups are involved. The…

检验相关矩阵最小特征根的相等性AI 解读

The asymptotic variance of a statistic used to test the equality of the smallest latent roots of a correlation matrix is computed. This permits an approximation to its null distribution suggested by Lawley (1956). A simulation is used to compare the performance of this approximation with others currently in use.

两个组的共同主成分子空间AI 解读

One important practical application of principal component analysis is to reduce a large number of variables, say p, to a smaller number, m, by making use of the first m principal components. This technique can easily be extended to two or more groups if the subspaces spanned by the first m principal components are the same for all groups. In this paper we develop an approximate procedure for testing such a hypothesis of common subspaces when two groups are involved. The…

若干维度检验统计量分布的最优界AI 解读

Optimal upper bounds are obtained for the distributions of two functions of the m - r smallest latent roots of HE−1, where E and H have Wishart distributions with identical covariance matrices; E has a central distribution while H has a noncentral distribution with unknown noncentrality matrix Δ of rank r. These bounds are then used to investigate the chi-squared approximation for some test criteria used in tests of dimensionality.

若干维数检验统计量分布的最优界AI 解读

Optimal upper bounds are obtained for the distributions of two functions of the m - r smallest latent roots of HE−1, where E and H have Wishart distributions with identical covariance matrices; E has a central distribution while H has a noncentral distribution with unknown noncentrality matrix Δ of rank r. These bounds are then used to investigate the chi-squared approximation for some test criteria used in tests of dimensionality.