Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality
نویسنده
چکیده
Asymptotic expansions of the distributions of typical estimators in canonical correlation analysis under nonnormality are obtained. The expansions include the Edgeworth expansions up to order O(1/n) for the parameter estimators standardized by the population standard errors, and the corresponding expansion by Hall’s method with variable transformation. The expansions for the Studentized estimators are also given using the Cornish–Fisher expansion and Hall’s method. The parameter estimators are dealt with in the context of estimation for the covariance structure in canonical correlation analysis. The distributions of the associated statistics (the structure of the canonical variables, the scaled log likelihood ratio and Rozeboom’s between-set correlation) are also expanded. The robustness of the normal-theory asymptotic variances of the sample canonical correlations and associated statistics are shown when a latent variable model holds. Simulations are performed to see the accuracy of the asymptotic results in finite samples. © 2007 Elsevier Inc. All rights reserved. AMS 1991 subject classification: 62E20; 62H20
منابع مشابه
Asymptotic Distributions of Estimators of Eigenvalues and Eigenfunctions in Functional Data
Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...
متن کاملAsymptotic expansions of the null distributions of test statistics for multivariate linear hypothesis under nonnormality
This paper is concerned with the distributions of some test statistics for a multivariate linear hypothesis under nonnormality. The test statistics considered include the likelihood ratio statistic, the Lawley-Hotelling trace criterion and the BartlettNanda-Pillai trace criterion, under normality. We derive asymptotic expansions of the null distributions of these test statistics up to the order...
متن کاملThe Efficiency of the Asymptotic Expansion of the Distribution of the Canonical Vector under Nonnormality
In canonical correlation analysis, canonical vectors are used in the interpretation of the canonical variables. We are interested in the asymptotic representation of the expectation, the variance and the distribution of the canonical vector. In this study, we derive the asymptotic distribution of the canonical vector under nonnormality. To obtain the asymptotic expansion of the canonical vector...
متن کاملAsymptotic expansions in the singular value decomposition for cross covariance and correlation under nonnormality
متن کامل
Conditions for Robustness to Nonnormality of Test Statistics in a GMANOVA Model
This paper discusses the conditions for robustness to the nonnormality of three test statistics for a general multivariate linear hypothesis, which were proposed under the normal assumption in a generalized multivariate analysis of variance (GMANOVA) model. Although generally the second terms in the asymptotic expansions of the mean and variance of the test statistics consist of skewness and ku...
متن کامل