HIGH-DIMENSIONAL NEWEY-POWELL TEST VIA APPROXIMATE MESSAGE PASSING

Area of Science:

• Econometrics
• Statistical Inference
• High-Dimensional Data Analysis

Background:

• The Newey and Powell (1987) heteroscedasticity test is a foundational tool.
• Extending classical statistical tests to high-dimensional settings presents significant challenges.
• Understanding data variance structure (homoscedasticity vs. heteroscedasticity) is crucial for reliable statistical modeling.

Purpose of the Study:

• To develop a high-dimensional extension of the Newey and Powell (1987) heteroscedasticity test.
• To establish the theoretical properties and practical performance of the proposed test.
• To apply the test to real-world economic and business datasets.

Main Methods:

• Expectile regression is employed as the core statistical framework.
• The proportional asymptotic regime ($n/p\to \delta \in (0,1]$) is considered for theoretical analysis.
• The approximate message passing algorithm is utilized for asymptotic analysis of the test statistic.

Main Results:

• The limiting distribution of the proposed test statistic is derived.
• The asymptotic power of the test is established.
• Extensive simulations demonstrate the test's numerical performance.
• Analysis of international economic growth data indicates homoscedasticity.
• Analysis of supermarket data reveals heteroscedasticity.

Conclusions:

• The proposed high-dimensional expectile regression-based test is a valuable extension for heteroscedasticity detection.
• The test demonstrates robust performance in simulations and practical applications.
• The findings contribute to the statistical toolkit for analyzing complex, high-dimensional datasets.