Introduction to Daniels (1954) Saddlepoint Approximations in Statistics View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1997

AUTHORS

Elvezio Ronchetti

ABSTRACT

Daniels’s paper provides at least three important contributions to statistics. From a methodological point of view, it introduces the use of saddlepoint techniques in statistics. These have proved to be a general and valuable tool for deriving very accurate approximations to the distribution of general estimators and test statistics both in parametric and nonparametric situations. Secondly, it shows the relationship between saddlepoint approximations and other approximations based on the seemingly unrelated idea of conjugate density. Finally, it derives a very accurate approximation of the density of the arithmetic mean of п independently identically distributed random variables. The main properties of this approximation are its simplicity and a relative error of order n-1 which leads to a very accurate approximation in small sample sizes and in the tails of the distribution. The fundamental ideas contained in Daniels’s paper carry over to complex situations and the characteristics of his approximation remain valid in a large variety of problems. More... »

PAGES

171-200

Book

TITLE

Breakthroughs in Statistics

ISBN

978-0-387-94989-5
978-1-4612-0667-5

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4612-0667-5_8

DOI

http://dx.doi.org/10.1007/978-1-4612-0667-5_8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1049261506


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