Work

Explaining the Saddlepoint Approximation

Year: 1999

Type: article

Abstract: Saddlepoint approximations are powerful tools for obtaining accurate expressions for densities and distribution functions. We give an elementary motivation and explanation of approximation techniques, starting with Taylor series expansions and progressing to the Laplace approximation of integrals. These approximations are illustrated with examples of the convolution of simple densities. We then turn to the saddlepoint approximation and, using both the Fourier inversion formula and Edgeworth expansions, we derive the saddlepoint approximation to the density of a single random variable. We next approximate the density of the sample mean of iid random variables, and also demonstrate the technique for approximating the density of a maximum likelihood estimator in exponential families.

Source: The American Statistician

DOI: 10.1080/00031305.1999.10474463

Authors: Constantino Goutis, George Casella

Institution: Cornell University

Language: English

Topic: Probability and Statistical Research

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Mathematical Sciences: Assessing Robustness of Inference