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Evaluating the density of ratios of noncentral quadratic forms in normal variables


Broda, Simon; Paolella, Marc S (2009). Evaluating the density of ratios of noncentral quadratic forms in normal variables. Computational Statistics and Data Analysis, 53(4):1264-1270.

Abstract

Two computable expressions for the exact density of a ratio of quadratic forms in Gaussian random vectors are derived, one of which is restricted to special cases of the problem. Ratios of this type are ubiquitous in econometrics, but their density, unlike the corresponding cumulative distribution function, has not received much attention to date. The new algorithms complement those available for the latter. The included performance study demonstrates the accuracy of the two algorithms, both absolute and relative to each other, and allows general recommendations on their use to be made.

Abstract

Two computable expressions for the exact density of a ratio of quadratic forms in Gaussian random vectors are derived, one of which is restricted to special cases of the problem. Ratios of this type are ubiquitous in econometrics, but their density, unlike the corresponding cumulative distribution function, has not received much attention to date. The new algorithms complement those available for the latter. The included performance study demonstrates the accuracy of the two algorithms, both absolute and relative to each other, and allows general recommendations on their use to be made.

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6 citations in Web of Science®
7 citations in Scopus®
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322 downloads since deposited on 16 Mar 2009
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Language:English
Date:15 February 2009
Deposited On:16 Mar 2009 14:28
Last Modified:05 Apr 2016 13:08
Publisher:Elsevier
ISSN:0167-9473
Publisher DOI:https://doi.org/10.1016/j.csda.2008.10.035

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