A Bartlett-type correction for likelihood ratio tests with application to testing equality of Gaussian graphical...

Area of Science:

• Statistics
• Statistical modeling
• Multivariate analysis

Background:

• Likelihood ratio tests are fundamental for hypothesis testing in statistical inference.
• Multivariate normal distributions are common in various scientific fields.
• Testing equality of distributions in high dimensions can be computationally challenging.

Purpose of the Study:

• To introduce a new correction for the likelihood ratio test in a two-sample multivariate normal setting.
• To extend the applicability of likelihood ratio tests to decomposable graphical models.

Main Methods:

• Development of a novel correction factor for the likelihood ratio test statistic.
• Application of the correction within the framework of decomposable graphical models.
• Demonstration of the test's decomposition into lower-dimensional problems.

Main Results:

• The proposed correction improves the accuracy of the likelihood ratio test for multivariate normal distributions.
• The method effectively handles the comparison of distributions in decomposable graphical models.
• The decomposition strategy simplifies the testing procedure.

Conclusions:

• The new correction offers a valuable advancement for statistical testing in multivariate contexts.
• This approach facilitates robust distribution equality testing in complex graphical models.
• The findings have implications for statistical analysis in fields utilizing multivariate normal data.