A Truncated Maximum Likelihood Estimator of a Constrained Bivariate Linear Regression Coefficient

Abstract

In a bivariate linear regression model, the constrained maximum likelihood estimator (MLE) of a regression coefficient usually has smaller variance than the unconstrained MLE. This situation can be reversed if both the sample size n and the correlation coefficient ρ of disturbances between two regression equations are small. That is, when both n and ρ are small, the variance of the unconstrained MLE is smaller than the constrained MLE. In this article, a truncated MLE is considered for the justification of using either the constrained or the unconstrained MLE as an appropriate estimator for the regression coefficient.

Key Words:

• Bivariate regression
• Constrained maximum likelihood estimation
• Truncated maximum likelihood estimation
• Modal approximation