Diagonal likelihood ratio test for equality of mean vectors in high-dimensional data

Area of Science:

• Statistics
• High-Dimensional Data Analysis

Background:

• Traditional methods for testing normal mean vectors struggle with high-dimensional data.
• Existing tests often require specific covariance matrix structures, limiting their applicability.

Purpose of the Study:

• To propose a flexible likelihood ratio test (LRT) framework for high-dimensional normal mean vectors.
• To address both one-sample and two-sample testing scenarios with equal covariance matrices.
• To offer an alternative to diagonal Hotelling's tests with improved characteristics.

Main Methods:

• Derivation of LRT statistics assuming diagonal covariance matrices.
• Analysis of test statistic properties, including summation of log-transformed squared t-statistics.
• Investigation of asymptotic normality without the diagonal covariance matrix assumption.

Main Results:

• The proposed LRT statistics exhibit unique properties compared to diagonal Hotelling's tests.
• Asymptotic normality is achieved without restrictive covariance matrix assumptions, enhancing flexibility.
• Simulation studies and real data analysis confirm the advantages of the proposed LRT methods.

Conclusions:

• The developed likelihood ratio test framework is highly flexible and practical for high-dimensional data.
• The method offers advantages over existing approaches, particularly in scenarios without strictly diagonal covariance matrices.
• The findings support the broader applicability of LRT in statistical inference for high-dimensional settings.