Accession Number:

ADA223280

Title:

Saddlepoint Approximations in Conditional Inference

Descriptive Note:

Corporate Author:

SOUTHERN METHODIST UNIV DALLAS TX DEPT OF STATISTICAL SCIENCE

Personal Author(s):

Report Date:

1990-06-11

Pagination or Media Count:

16.0

Abstract:

Conditional inference plays an important role in statistical inference. The conditionality principle has been used to deal with various problems. One major step in the procedure of conditional inference is to obtain the conditional distribution functions. As is often the case, the exact conditional distributions are difficult or impossible to obtain, and conventional approximations may often fail to work. For example, generally it is hard to calculate the moments of the conditional distributions which are necessary quantities for the Edgeworth approximations. Furthermore, these approximations are often unsatisfactory for small or moderate sample sizes. On the other hand, it is well known that saddlepoint expansions lead to accurate approximations, even for small sample sizes. This paper derives accurate saddlepoint expansions for the case of nonlinear conditioning. The results include Skovgaards 1987 method as a special case when the distribution is continuous, but have much broader applications. Sections 2 and 3 expand saddlepoint formulas for the conditional density and conditional distribution function, respectively. Two examples are considered in Section 4 to illustrate the use of the new results. Extraordinary accuracy is also shown numerically. kr

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE