Imperial College London
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ProfessorNiallAdams

Faculty of Natural Sciences, Department of Mathematics

Professor of Statistics
 
 
 
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Contact

 

+44 (0)20 7594 8837n.adams Website

 
 
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Location

 

6M55Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Adams:2015:10.1007/s11222-015-9583-4,
author = {Adams, NM and Bodenham, DA},
doi = {10.1007/s11222-015-9583-4},
journal = {Statistics and Computing},
pages = {917--928},
title = {A comparison of efficient approximations for a weighted sum of chi-squared random variables},
url = {http://dx.doi.org/10.1007/s11222-015-9583-4},
volume = {26},
year = {2015}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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.
AU  - Adams,NM
AU  - Bodenham,DA
DO  - 10.1007/s11222-015-9583-4
EP  - 928
PY  - 2015///
SN  - 0960-3174
SP  - 917
TI  - A comparison of efficient approximations for a weighted sum of chi-squared random variables
T2  - Statistics and Computing
UR  - http://dx.doi.org/10.1007/s11222-015-9583-4
UR  - http://hdl.handle.net/10044/1/23319
VL  - 26
ER  -
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