Saddlepoint approximation in the linear structural relationship model

Abstract

It is shown that the joint maximum likelihood estimator of slope and intercept of the regression line in the classical (known error-variance ratio) linear structural relationship model can be represented as a solution of a two- dimensional M- equation. Therefore, it is possible to use a general saddlepoint approximation for multidimensional M- equations. Under normality assumptions we express the solution of the implicit multivariate “centering equation” in an explicit form. This allows a considerable saving of computing time. By integrating out numerically an unwanted variable one is also able to find the saddlepoint approximation for the slope- estimator. Numerical examples illustrate the efficiency of the approximation.