Improved estimators of regression coefficients in measurement error models

Abstract

In the theory of regression analysis, it is well known that the presence of measurement errors in the explanatory variables makes the ordinary least squares estimator (OLSE) biased and inconsistent, and the maximum likelihood estimator (MLE) is not obtainable without restrictive assumptions. We develop mixed-type estimators, which combine OLSE and MLE and compromise between them, utilizing a preliminary test or weighting function of a test statistic. It is shown that the weighting function estimators are superior to the classical estimators in terms of mean square errors in a large parameter space.

Keywords:

• Maximum likelihood estimator
• ordinary least squares estimator
• preliminary test estimators
• weighting function estimators

^∗Now at Fu Jen University, Taipei, Taiwan.

^∗Now at Fu Jen University, Taipei, Taiwan.

Notes

^∗Now at Fu Jen University, Taipei, Taiwan.