Exact and Approximate Distributions of the Maximum Likelihood Estimator of a Slope Coefficient: The LIML Estimator for a Known Covariance Matrix

Abstract

When the errors are normally independently distributed with equal variance, the maximum likelihood estimator of the slope of a linear functional relationship is the slope of the line minimizing the sum of squared deviations orthogonal to the line. The exact density and distribution of this estimator are obtained. Approximate distributions are obtained, and their accuracies are discussed