Improving the Maximum Likelihood Estimate in Linear Functional Relationships for Alternative Parameter Sequences

Abstract

We propose an improvement of the maximum likelihood (ML) estimate in linear functional relationships. The improved estimate is a linear combination of the ML and the least squares estimate so as to remove the bias of the former. Approximations to the distribution of the estimate are derived for two alternative parameter sequences: a sequence in which the noncentrality parameter (the spread of the true values) increases while the number of observations stays fixed, and that in which the number of observations increases. The mean squared errors of the improved estimate, in terms of its asymptotic distributions, are obtained and shown to be smaller than those of the ML. Implications to large-scale simultaneous econometric models are also given.

Key Words:

• Linear functional relationships
• Maximum likelihood estimate
• Least squares estimate
• Reduction of bias
• Reduction of mean squared errors
• Simultaneous equation econometric model