A study of two high-dimensional likelihood ratio tests under alternative hypotheses

2018 ◽  
Vol 07 (01) ◽  
pp. 1750016 ◽  
Author(s):  
Huijun Chen ◽  
Tiefeng Jiang

Let [Formula: see text] be a [Formula: see text]-dimensional normal distribution. Testing [Formula: see text] equal to a given matrix or [Formula: see text] equal to a given pair through the likelihood ratio test (LRT) is a classical problem in the multivariate analysis. When the population dimension [Formula: see text] is fixed, it is known that the LRT statistics go to [Formula: see text]-distributions. When [Formula: see text] is large, simulation shows that the approximations are far from accurate. For the two LRT statistics, in the high-dimensional cases, we obtain their central limit theorems under a big class of alternative hypotheses. In particular, the alternative hypotheses are not local ones. We do not need the assumption that [Formula: see text] and [Formula: see text] are proportional to each other. The condition [Formula: see text] suffices in our results.

2010 ◽  
Vol 107 (2) ◽  
pp. 501-510 ◽  
Author(s):  
Michael A. Long ◽  
Kenneth J. Berry ◽  
Paul W. Mielke

Monte Carlo resampling methods to obtain probability values for chi-squared and likelihood-ratio test statistics for multiway contingency tables are presented. A resampling algorithm provides random arrangements of cell frequencies in a multiway contingency table, given fixed marginal frequency totals. Probability values are obtained from the proportion of resampled test statistic values equal to or greater than the observed test statistic value.


1987 ◽  
Vol 36 (3-4) ◽  
pp. 125-140
Author(s):  
Lily Llorens Mantelle ◽  
Malay Ghosh

The paper considers generalized likelihood ratio tests for the equality of the location, parameters and⁄or the failure rates of k independent location and scale parameter exponentials when observations are censored in time. For testing the equality of the failure rates, asymptotic null distributions of the generalized likelihood ratio test (GLRT) criteria are obtained. Also, asymptotic distributions of GLRT criteria are obtained under local alternatives. For testing the equality of the location parameters, asymptotic null distributions of the GLRT criteria are obtained.


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