A comparison of efficient approximations for a weighted sum of chi-squared random variables
File(s)
Published version
Author(s)
Adams, NM
Bodenham, DA
Type
Journal Article
Abstract
In many applications, the cumulative distribution function (cdf) FQNFQN of a positively weighted sum of N i.i.d. chi-squared random variables QNQN is required. Although there is no known closed-form solution for FQNFQN, there are many good approximations. When computational efficiency is not an issue, Imhof’s method provides a good solution. However, when both the accuracy of the approximation and the speed of its computation are a concern, there is no clear preferred choice. Previous comparisons between approximate methods could be considered insufficient. Furthermore, in streaming data applications where the computation needs to be both sequential and efficient, only a few of the available methods may be suitable. Streaming data problems are becoming ubiquitous and provide the motivation for this paper. We develop a framework to enable a much more extensive comparison between approximate methods for computing the cdf of weighted sums of an arbitrary random variable. Utilising this framework, a new and comprehensive analysis of four efficient approximate methods for computing FQNFQN is performed. This analysis procedure is much more thorough and statistically valid than previous approaches described in the literature. A surprising result of this analysis is that the accuracy of these approximate methods increases with N.
Date Issued
2015-06-14
Date Acceptance
2015-05-22
Citation
Statistics and Computing, 2015, 26 (4), pp.917-928
ISSN
0960-3174
Publisher
Springer Verlag
Start Page
917
End Page
928
Journal / Book Title
Statistics and Computing
Volume
26
Issue
4
Copyright Statement
© The Author(s) 2015. This article is published with open access at Springerlink.com
License URL
Subjects
Science & Technology
Technology
Physical Sciences
Computer Science, Theory & Methods
Statistics & Probability
Computer Science
Mathematics
Approximation
Moment-matching
Streaming data
QUADRATIC-FORMS
DISTRIBUTIONS
STATISTICS
VARIANCE
MIXTURES
0104 Statistics
0802 Computation Theory And Mathematics
Publication Status
Published