Robustness Property of Robust-BD Wald-Type Test for Varying-Dimensional General Linear Models

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Robust inference is crucial for reliable statistical analysis, especially with imperfect data.
• Existing methods for robust inference are often limited to finite-dimensional settings and specific loss functions.
• Contaminated data can significantly impact the stability of test statistics' asymptotic level and power.

Purpose of the Study:

• To investigate the stability of asymptotic level and power of test statistics with contaminated data in general linear models.
• To introduce and analyze a novel robust Wald-type test using robust error measures (robust-BD) for diverging parameter dimensions.
• To assess the robustness of validity and efficiency of the proposed test under various contamination scenarios.

Main Methods:

• Derivation of the influence function for the robust-BD parameter estimator under regularity conditions.
• Asymptotic analysis of the robust-BD Wald-type test statistic.
• Evaluation of the test's performance under small data contamination and in the neighborhood of contiguous alternatives.

Main Results:

• The robust-BD parameter estimator's influence function was successfully derived.
• The robust-BD Wald-type test demonstrates asymptotic robustness of validity, maintaining a stable level under null hypothesis contamination.
• The test exhibits sufficient asymptotic power under contaminated distributions near contiguous alternatives.

Conclusions:

• The proposed robust-BD Wald-type test offers a reliable solution for statistical inference in general linear models with contaminated data.
• The findings support the practical utility of the robust-BD test, showing its stability and efficiency in challenging data conditions.
• This research extends robust inference methodologies to higher-dimensional settings and a broader class of error measures.