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Saddlepoint approximations for noncentral quadratic forms

Marsh, P.W.N. (1998) Saddlepoint approximations for noncentral quadratic forms. Econometric Theory. pp. 539-559. ISSN 0266-4666

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Abstract

Many estimators and tests are of the form of a ratio of quadratic forms in normal variables. Excepting a few very special cases little is known about the density or distribution of these ratios, particularly if we allow for noncentrality in the quadratic forms. This paper assumes this generality and derives saddlepoint approximations for this class of statistics. We first derive and prove the existence of an exact inversion based on the joint characteristic function. Then the saddlepoint algorithm is applied and the leading term found, and analytic justification of the asymptotic nature of the approximation is given. As an illustration we consider the calculation of sizes and powers of F-tests, where a new exact result is found.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 1998 Cambridge University Press
Academic Units: The University of York > Economics and Related Studies (York)
Depositing User: Sherpa Assistant
Date Deposited: 19 Aug 2005
Last Modified: 17 Oct 2013 14:40
Published Version: http://dx.doi.org/10.1017/S0266466698145012
Status: Published
Refereed: Yes
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/594

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