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 L1 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. © 1991 Biometrika Trust.