Linear regression analysis with inequality constraints on the regression parameters via empirical likelihood

Abstract

An empirical likelihood ratio test is developed for testing for or against inequality constraints on regression parameters in linear regression analysis. The proposed approach imposes no parametric model nor identically distributing assumption on the random errors. The asymptotic distribution of the proposed test statistic under null hypothesis is shown to be of chi-bar-squared type. The asymptotic power under contiguous alternatives is also briefly discussed. Moreover, an adjusted empirical likelihood method is adopted to improve the small sample size behaviour of the proposed test. Several simulation studies are carried out to assess the finite sample performance of the proposed tests. The results reveal that the proposed tests could be valuable for improving inference efficiency. A real-life example is discussed to illustrate the theoretical results.

Keywords:

• chi-bar-squared distribution
• empirical likelihood
• inequality constraints
• linear regression analysis

AMS Subject Classification:

• 62J05
• 62E20

Funding

The authors thank the Associate Editor and an anonymous referee for their insightful comments that have led to significant improvements.