Testing Equality Of Covariance Matrices Research Articles

Functional test for high-dimensional covariance matrix, with application to mitochondrial calcium concentration

In this paper, we present a novel method to test equality of covariance matrices of two high-dimensional samples. The methodology applies the idea of functional data analysis into high-dimensional data study. Asymptotic results of the proposed method are established. Some simulation studies are conducted to investigate the finite sample performance of the proposed method. We illustrate our testing procedures on a mitochondrial calcium concentration data for testing equality of covariance matrices.

Set-based differential covariance testing for genomics.

The problem of detecting the changes in covariance for a single pair of genomic features has been studied in some detail but may be limited in importance or general applicability. For testing equality of covariance matrices of a set of features, many methods have been limited to the two‐sample problem and involve varying assumptions on the number of features p versus the sample size n. More general covariance regression approaches are appealing but have been insufficiently structured to provide interpretable testing. To address these deficiencies, we propose a simple uniform framework to test association of covariance matrices with an experimental variable, whether discrete or continuous. We describe four different summary statistics, to ensure power and flexibility under various alternatives, including a new “connectivity” statistic that is sensitive to the changes in overall covariance magnitude. For continuous experimental variables, a natural individual “risk score” is associated with several of the statistics. We establish asymptotic results applicable to both continuous and discrete responses, with relatively mild conditions and allowing for situations where p>n. We also show that the proposed statistics are permutationally equivalent to some existing methods in the two‐sample special case. We demonstrate the power and utility of our approaches via simulation and analysis of real data. The R package CorDiff is published on R CRAN.

Percentage points of LRC for testing equality of covariance matrices under intraclass correlation structure

ABSTRACTThe exact null distribution of the likelihood ratio test statistic for testing equality of covariance matrices of q compound symmetric Gaussian models (bivariate or trivariate) has been obtained and percentage points for q ⩽ 5 have been computed. The inverse Mellin transform and calculus of residues have been used to derive these results.

Testing Equality of Covariance Matrices via Pythagorean Means

We provide a new test for equality of covariance matrices that leads to a convenient mechanism for testing specification using the information matrix equality. The test relies on a new characterization of equality between twok dimensional positive-definite matrices A and B : the traces of AB 1 and BA 1 are equal tok if and only if A = B. Using this criterion, we introduce a class of omnibus test statistics for equality of covariance matrices and examine their null, local, and global approximations under some mild regularity conditions. Monte Carlo experiments are conducted to explore the performance characteristics of the test criteria and provide comparisons with existing tests under the null hypothesis and local and global alternatives. The tests are applied to the classic empirical models for voting turnout investigated by Wolfinger and Rosenstone (1980) and Nagler (1991, 1994). Our tests show that all classic models for the 1984 presidential voting turnout are misspecified in the sense that the information matrix equality fails.

MANOVA with Summary Statistics: A Stata Program

Almost all available statistical packages are capable of performing Multivariate Analysis of Variance (MANOVA) from raw data. Some of statistical packages have capability to perform independent sample t-test, ANOVA and some other tests of significance on summary data, but you come across not single software that has the capability to perform MANOVA directly on summary data. A STATA programme has been written to perform Multivariate ANOVA on summary data. The programme computes available statistics for Multivariate ANOVA (i.e Willk’s Lembda, Lawley’s-Hotelling trace, Pillae’s trace and Roy’s largest root). The programme is also capable to perform Box–M test for testing equality of covariance matrices on summary data. Example has been given by using the programme on summary data to perform Multivariate ANOVA.

MANOVA with Summary Statistics: A STATA Program

Almost all available statistical packages are capable of performing Multivariate Analysis of Variance (MANOVA) from raw data. Some of statistical packages have capability to perform independent sample t-test, ANOVA and some other tests of significance on summary data, but you come across not single software that has the capability to perform MANOVA directly on summary data. A STATA programme has been written to perform Multivariate ANOVA on summary data. The programme computes available statistics for Multivariate ANOVA (i.e Willk’s Lembda, Lawley’s-Hotelling trace, Pillae’s trace and Roy’s largest root). The programme is also capable to perform Box–M test for testing equality of covariance matrices on summary data. Example has been given by using the programme on summary data to perform Multivariate ANOVA.

Testing equality of covariance matrices when data are incomplete

In the statistics literature, a number of procedures have been proposed for testing equality of several groups’ covariance matrices when data are complete, but this problem has not been considered for incomplete data in a general setting. This paper proposes statistical tests for equality of covariance matrices when data are missing. A Wald test (denoted by T 1 ), a likelihood ratio test (LRT) (denoted by R), based on the assumption of normal populations are developed. It is well-known that for the complete data case the classic LRT and the Wald test constructed under the normality assumption perform poorly in instances when data are not from multivariate normal distributions. As expected, this is also the case for the incomplete data case and therefore has led us to construct a robust Wald test (denoted by T 2 ) that performs well for both normal and non-normal data. A re-scaled LRT (denoted by R * ) is also proposed. A simulation study is carried out to assess the performance of T 1 , T 2 , R, and R * in terms of closeness of their observed significance level to the nominal significance level as well as the power of these tests. It is found that T 2 performs very well for both normal and non-normal data in both small and large samples. In addition to its usual applications, we have discussed the application of the proposed tests in testing whether a set of data are missing completely at random (MCAR).

Distribution of the likelihood ratio statistic for testing homogeneity of covariance matrices of completely symmetric Gaussian models

In this article the distribution of the likelihood ratio test statistic for testing equality of covariance matrices of completely symmetric Gaussian models has been derived in beta series. Comparison of results with the exact results has also been done.

Robust Procedures for Testing Equality of Covariance Matrices

Normal-theory tests for common variance are very sensitive to departures from normality in both univariate and multivariate applications. For mild departures from normality and moderate sample size, nominal a = .01 produced Type I error rates in excess of .20 in simulation studies. Since a modification of Levene's test has been shown to perform well for the univariate problem, two multivariate generalizations of this test are proposed. Both procedures are robust to departures from normality, and are simple computationally. Comparisons of the power of these two procedures and a procedure proposed previously by Tiku and Balakrishnan (1985, Communications in StatisticsTheory and Methods 14, 3033-3051) indicate that the three methods should be viewed as complementary.

Bootstrap Critical Values for Testing Homogeneity of Covariance Matrices

Abstract Bartlett's modified likelihood ratio statistic A is often suggested in multivariate analysis for testing equality of covariance matrices. Unfortunately, the χ 2-approximation to the null distribution of −2 log Λ is useful only when the data is normally distributed. This article presents a pooled bootstrap procedure that replaces the χ 2-approximation and makes Bartlett's statistic a useful tool for data analysis. This procedure also applies to most quadratic form test statistics.

NONNULL DISTRIBUTION OF LRC FOR TESTING HOMOGENEITY OF COVARIANCE MATRICES OF COMPLETELY SYMMETRIC GAUSSIAN MODELS


 
 
 The nonnull moments of the likelihood ratio statistic for testing equality of covariance matrices of completely symmetric Gaussian models are obta.ined in terms of the Lauricella's hypergeometric functions and also in terms of zonal polynomials. Then the nonnull asymptotic distribution of the statistic is derived under certain alternatives for unequal samples. 
 
 

Asymptotic nonnull distribution of the likelihood ratio statistic for testing equality of covariance matrices under intraclass correlation model

In this paper the asymptotic nonnull distribution of the likelihood ratio statistic for testing equality of covariance matrices under intraclass correlation structure is derived under certain alternatives for unequal samples.

Nonnull distribution of the likelihood ratio criterion for testing equality of covariance matrices under intraclass correlation model

The nonnull moments of the likelihood ratio statistic for testing equality of covariance matrices under intraclass correlation structure are obtained in terms of the Lauricella's hypergeometric functions and also in terms of zonal polynomials. Then the nonnull asymptotic distribution of the statistic is derived for certain alternatives.

Distribution of Likelihood Ratio Statistic for Testing Equality of Covariance Matrices of Multivariate Gaussian Models

Distribution of Likelihood Ratio Statistic for Testing Equality of Covariance Matrices of Multivariate Gaussian Models

Distribution of likelihood ratio statistic for testing equality of covariance matrices of multivariate Gaussian models

SUMMARY In this paper the exact distribution of the likelihood ratio statistic for testing equality of covariance matrices of multivariate Gaussian models has been derived. Percentage points of the test statistic have also been tabulated.