TESTING HIGH-DIMENSIONAL REGRESSION COEFFICIENTS IN LINEAR MODELS.

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• High-dimensional linear regression models are widely used but present statistical inference challenges.
• Existing methods for testing regression coefficients may lack sufficient power and efficiency.

Purpose of the Study:

• To propose a novel statistical test for the coefficient vector in high-dimensional linear regression.
• To establish the asymptotic properties and efficiency of the new test.
• To demonstrate the practical utility and performance of the proposed method.

Main Methods:

• Development of a new test statistic for the coefficient vector.
• Asymptotic normality established using the martingale central limit theorem.
• Asymptotic relative efficiency (ARE) derived and compared to existing methods.

Main Results:

• The proposed test statistic exhibits asymptotic normality.
• The ARE is shown to be greater than or equal to one under local alternatives.
• Numerical studies indicate excellent Type I error rate control.
• The proposed test demonstrates superior power compared to existing methods.

Conclusions:

• The new statistical test provides a powerful and efficient tool for inference in high-dimensional linear models.
• The method is validated through simulations and a real-data example.
• This work advances statistical inference techniques for complex regression settings.