Saddlepoint approximations for regression models

Abstract

SUMMARY This paper uses the techniques of saddlepoint or tilted-exponential approximation to develop an approximation to the small-sample distribution of estimators defined by a system of estimating equations when observations are independently but not identically distributed. This allows for the explicit treatment of models with explanatory variables. The approximation is applied to L 1 regression, and the accuracy of the approximation is demonstrated in a case in which the usual normal approximation is very poor. An analysis of the example indicates the usefulness of a new variant of exponential tilting in calculating the transformation measure, a quantity which plays an important role in assuring the accuracy of the approximation.