Cornell University

Monday, March 3,1997

2:30 pm - refreshments

3:00 pm - talk

(Please note deviation from usual times)

Room 327, Yost Hall

Abstract

Saddlepoint approximations are highly accurate tools for approximating the density or distribution of a statistic, in particular a statistic that is found using an estimating equation. In the classical theory of saddlepoint approximations, it is assumed that the cumulant generating function of the underlying density is known, yielding approximations which have a relative error of order O(n-312). This translates into excellent accuracy even for small sample sizes.

However, as the cumulant generating function will typically depend on the unknown parameters, these parameters must be estimated. This in turn can greatly reduce the attainable accuracy. We present a theorem which shows that the accuracy of the saddlepoint approximation is governed by the accuracy of the point estimates. We also examine the performance of a number of other methods that have been proposed for estimating the cumulant generating function. The case of the sample mean is investigated for a couple of specific distributions. The loss of accuracy due to estimation and possible fixes are discussed with comparisons to the bootstrap. We indicate where and how it is possible to increase accuracy, even when the parameters are unknown.