scholarly journals Testing the equality of mean vectors for paired doubly multivariate observations in blocked compound symmetric covariance matrix setup

2015 ◽  
Vol 137 ◽  
pp. 50-60 ◽  
Author(s):  
Anuradha Roy ◽  
Ricardo Leiva ◽  
Ivan Žežula ◽  
Daniel Klein
Keyword(s):  
Covariance Matrix ◽  
Mean Vectors ◽  
Equality Of Mean Vectors

Robustness of Yao’s, James’, and Johansen’s Tests Under Variance-Covariance Heteroscedasticity and Nonnormality

1991 ◽  
Vol 16 (2) ◽  
pp. 125-139 ◽  
Author(s):  
James Algina ◽  
Takako C. Oshima ◽  
K. Linda Tang
Keyword(s):  
Type I Error ◽  
Error Rates ◽  
Second Order ◽  
Type I ◽  
Lognormal Distributions ◽  
First Order ◽  
Type I Error Rates ◽  
Mean Vectors ◽  
Equality Of Mean Vectors

Type I error rates for Yao’s, James’ first order, James’ second order, and Johansen’s tests of equality of mean vectors for two independent samples were estimated for various conditions defined by the degree of heteroscedasticity and nonnormality (uniform, Laplace, t(5), beta (5, 1.5), exponential, and lognormal distributions). For these alternatives to Hotelling’s T2, variance-covariance homogeneity is not an assumption. Although the four procedures can be seriously nonrobust with exponential and lognormal distributions, they were fairly robust with the rest of the distributions. The performance of Yao’s test, James’ second order test, and Johansen’s test was slightly superior to the performance of James’ first order test.

scholarly journals Near-Exact Distributions for Likelihood Ratio Statistics Used in the Simultaneous Test of Conditions on Mean Vectors and Patterns of Covariance Matrices

2016 ◽  
Vol 2016 ◽  
pp. 1-25 ◽  
Author(s):  
Carlos A. Coelho ◽  
Filipe J. Marques ◽  
Sandra Oliveira
Keyword(s):  
Covariance Matrix ◽  
Likelihood Ratio ◽  
Exact Distribution ◽  
Covariance Matrices ◽  
Distribution Functions ◽  
Small Samples ◽  
Chi Square ◽  
Exact Distributions ◽  
Mean Vectors ◽  
Likelihood Ratio Statistics

The authors address likelihood ratio statistics used to test simultaneously conditions on mean vectors and patterns on covariance matrices. Tests for conditions on mean vectors, assuming or not a given structure for the covariance matrix, are quite common, since they may be easily implemented. But, on the other hand, the practical use of simultaneous tests for conditions on the mean vectors and a given pattern for the covariance matrix is usually hindered by the nonmanageability of the expressions for their exact distribution functions. The authors show the importance of being able to adequately factorize the c.f. of the logarithm of likelihood ratio statistics in order to obtain sharp and highly manageable near-exact distributions, or even the exact distribution in a highly manageable form. The tests considered are the simultaneous tests of equality or nullity of means and circularity, compound symmetry, or sphericity of the covariance matrix. Numerical studies show the high accuracy of the near-exact distributions and their adequacy for cases with very small samples and/or large number of variables. The exact and near-exact quantiles computed show how the common chi-square asymptotic approximation is highly inadequate for situations with small samples or large number of variables.

Testing Equality of Mean Vectors in Two Sample Problem with Missing Data

2010 ◽  
Vol 39 (3) ◽  
pp. 487-500 ◽  
Author(s):  
Nobumichi Shutoh ◽  
Makiko Kusumi ◽  
Wataru Morinaga ◽  
Shunichi Yamada ◽  
Takashi Seo
Keyword(s):  
Missing Data ◽  
Sample Problem ◽  
Two Sample Problem ◽  
Mean Vectors ◽  
Equality Of Mean Vectors
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