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Biostatistics Advance Access originally published online on August 29, 2007
Biostatistics 2008 9(2):321-332; doi:10.1093/biostatistics/kxm030
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© The Author 2007. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Small-sample estimation of negative binomial dispersion, with applications to SAGE data

Mark D. Robinson*

Bioinformatics Division, The Walter and Eliza Hall Institute of Medical Research, 1G Royal Parade, Parkville, Victoria 3050, Australia and Department of Medical Biology, The University of Melbourne, Parkville, Victoria 3010, Australia mrobinson{at}wehi.edu.au

Gordon K. Smyth

Bioinformatics Division, The Walter and Eliza Hall Institute of Medical Research, 1G Royal Parade, Parkville, Victoria 3050, Australia

* To whom correspondence should be addressed.

We derive a quantile-adjusted conditional maximum likelihood estimator for the dispersion parameter of the negative binomial distribution and compare its performance, in terms of bias, to various other methods. Our estimation scheme outperforms all other methods in very small samples, typical of those from serial analysis of gene expression studies, the motivating data for this study. The impact of dispersion estimation on hypothesis testing is studied. We derive an "exact" test that outperforms the standard approximate asymptotic tests.

Keywords: Conditional likelihood; Dispersion; Negative binomial; Quantile adjustment; Serial analysis of gene expression

Received October 17, 2006; revised April 24, 2007; revised June 9, 2007; accepted for publication July 19, 2007.


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