A robust testing procedure for the equality of covariance matrices
نویسندگان
چکیده
In classical statistics the likelihood ratio statistic used in testing hypotheses about covariance matrices does not have a closed form distribution, but asymptotically under strong normality assumptions is a function of the 2-distribution. This distributional approximation totally fails if the normality assumption is not completely met. In this paper we will present multivariate robust testing procedures for the scatter matrix using S-estimates. We modify the classical likelihood ratio test (LRT) into a robust LRT by substituting the robust estimates in the formula in place of classical estimates. A nonlinear formula is also suggested to approximate the degrees of freedom for the approximated Wishart distribution proposed for S-estimates of the shape matrix . We present simulation results to compare the validity and the efficiency of the robust likelihood test to the classical likelihood test. © 2004 Elsevier B.V. All rights reserved.
منابع مشابه
Tests of some hypotheses on characteristic roots of covariance matrices not requiring normality assumptions
Test statistics for testing some hypotheses on characteristic roots of covariance matrices are presented, their asymptotic distribution is derived and a confidence interval for the proportional sum of the characteristic roots is constructed. The resulting procedures are robust against violation of the normality assumptions in the sense that they asymptotically possess chosen significance level ...
متن کاملComparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering.
Comparing large covariance matrices has important applications in modern genomics, where scientists are often interested in understanding whether relationships (e.g., dependencies or co-regulations) among a large number of genes vary between different biological states. We propose a computationally fast procedure for testing the equality of two large covariance matrices when the dimensions of t...
متن کاملResampling-based methods in single and multiple testing for equality of covariance/correlation matrices.
Traditional resampling-based tests for homogeneity in covariance matrices across multiple groups resample residuals, that is, data centered by group means. These residuals do not share the same second moments when the null hypothesis is false, which makes them difficult to use in the setting of multiple testing. An alternative approach is to resample standardized residuals, data centered by gro...
متن کاملOn Selecting Tests for Equality of Two Normal Mean Vectors.
The conventional approach for testing the equality of two normal mean vectors is to test first the equality of covariance matrices, and if the equality assumption is tenable, then use the two-sample Hotelling T (2) test. Otherwise one can use one of the approximate tests for the multivariate Behrens-Fisher problem. In this article, we study the properties of the Hotelling T (2) test, the conven...
متن کاملError bounds for high–dimensional Edgeworth expansions for some tests on covariance matrices
Problems of testing three hypotheses : (i) equality of covariance matrices of several multivariate normal populations, (ii) sphericity, and (iii) that a covariance matrix is equal to a specified one, are treated. High–dimensional Edgeworth expansions of the null distributions of the modified likelihood ratio test statistics are derived. Computable error bounds of the expansions are derived for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computational Statistics & Data Analysis
دوره 49 شماره
صفحات -
تاریخ انتشار 2005