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Saddlepoint approximations in conditional inference

Published online by Cambridge University Press:  14 July 2016

Suojin Wang*
Affiliation:
Texas A&M University
*
∗∗ Postal address: Department of Statistics, Texas A&M University, College Station, TX 77843, USA.

Abstract

Saddlepoint approximations are derived for the conditional cumulative distribution function and density of where is the sample mean of n i.i.d. bivariate random variables and g(x, y) is a non-linear function. The relative error of order O(n–1) is retained. The results extend the important work of Skovgaard (1987), and are useful in conditional inference, especially in the case of small or moderate sample sizes. Generalizations to higher-dimensional random vectors are also discussed. Some examples are demonstrated.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1993 

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