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

Huijun Chen, Tiefeng Jiang

Research output: Contribution to journalArticle

Abstract

Let Np(μ,∑) be a p-dimensional normal distribution. Testing ∑ equal to a given matrix or (μ,∑) equal to a given pair through the likelihood ratio test (LRT) is a classical problem in the multivariate analysis. When the population dimension p is fixed, it is known that the LRT statistics go to 2-distributions. When p 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 p and n are proportional to each other. The condition n - 1 > p ∞ suffices in our results.

LanguageEnglish (US)
Article number1750016
JournalRandom Matrices: Theory and Application
Volume7
Issue number1
DOIs
StatePublished - Jan 1 2018

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Likelihood Ratio Test Statistic
Multivariate Functions
Multivariate Normal Distribution
Likelihood Ratio Test
High-dimensional Data
Central limit theorem
High-dimensional
Multivariate Analysis
Alternatives
Gaussian distribution
Directly proportional
Testing
Approximation
Simulation
Multivariate normal distribution
Likelihood ratio test
Test statistic
Class

Keywords

  • alternative hypothesis
  • central limit theorem
  • high-dimensional data
  • Likelihood ratio test
  • multivariate Gamma function
  • multivariate normal distribution

Cite this

A study of two high-dimensional likelihood ratio tests under alternative hypotheses. / Chen, Huijun; Jiang, Tiefeng.

In: Random Matrices: Theory and Application, Vol. 7, No. 1, 1750016, 01.01.2018.

Research output: Contribution to journalArticle

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