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Kernel density-based likelihood ratio tests for linear regression models.

Feifei Yan1, Qing-Song Xu1, Man-Lai Tang2

  • 1School of Mathematics and Statistics, Central South University, Changsha, China.

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|October 5, 2020
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Summary
This summary is machine-generated.

A new profile likelihood ratio test (PLRT) for multiple linear regression models offers improved performance over existing methods. This statistical test does not require assumptions about error distribution, enhancing its applicability and power in various data analyses.

Keywords:
Wilks phenomenonlikelihood ratio testprofile likelihood ratio testsemiparametric approach

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Area of Science:

  • Statistics
  • Econometrics
  • Data Science

Background:

  • Traditional likelihood ratio tests (LRT) for multiple linear regression models often require specific assumptions about the distribution of errors.
  • These assumptions can limit the applicability and performance of LRT in real-world scenarios where error distributions may be unknown or non-standard.

Purpose of the Study:

  • To develop a novel profile likelihood ratio test (PLRT) for multiple linear regression that is robust to unspecified error distributions.
  • To evaluate the statistical properties and performance of the proposed PLRT compared to existing methods.

Main Methods:

  • Development of a profile likelihood ratio test (PLRT) based on estimated error density for multiple linear regression.
  • Asymptotic properties of the PLRT were derived, including an investigation of the Wilks phenomenon.
  • Extensive simulation studies were conducted to assess the PLRT's performance against established LRT, empirical likelihood ratio test, and weighted profile likelihood ratio test.

Main Results:

  • The proposed PLRT demonstrated superior performance compared to existing methods, exhibiting type I error rates closer to nominal levels.
  • PLRT generally achieved higher statistical power and showed satisfactory performance even when error distributions lacked existing moments, such as the Cauchy distribution.
  • The PLRT exhibited a higher probability of correctly selecting models in multiple testing scenarios.

Conclusions:

  • The developed PLRT provides a more robust and powerful alternative for hypothesis testing in multiple linear regression models, especially when error distributions are unknown.
  • The method's ability to handle non-standard error distributions and its improved performance in model selection highlight its practical utility.
  • The study validates the effectiveness of PLRT through simulations and real-world data analyses, including gene expression and material science datasets.