Joint estimation of the mean and error distribution in generalized linear models

Huang, Alan (2014) Joint estimation of the mean and error distribution in generalized linear models. Journal of The American Statistical Association, 109 505: 186-196. doi:10.1080/01621459.2013.824892


Author Huang, Alan
Title Joint estimation of the mean and error distribution in generalized linear models
Journal name Journal of The American Statistical Association   Check publisher's open access policy
ISSN 0162-1459
1537-274X
Publication date 2014-01-01
Year available 2013
Sub-type Article (original research)
DOI 10.1080/01621459.2013.824892
Volume 109
Issue 505
Start page 186
End page 196
Total pages 11
Place of publication Alexandria, VA, United States
Publisher American Statistical Association
Language eng
Formatted abstract
This article introduces a semiparametric extension of generalized linear models that is based on a full probability model, but does not require specification of an error distribution or variance function for the data. The approach involves treating the error distribution as an infinite-dimensional parameter, which is then estimated simultaneously with the mean-model parameters using a maximum empirical likelihood approach. The resulting estimators are shown to be consistent and jointly asymptotically normal in distribution. When interest lies only in inferences on the mean-model parameters, we show that maximizing out the error distribution leads to profile empirical log-likelihood ratio statistics that have asymptotic χ2 distributions under the null. Simulation studies demonstrate that the proposed method can be more accurate than existing methods that offer the same level of flexibility and generality, especially with smaller sample sizes. The theoretical and numerical results are complemented by a data analysis example. Supplementary materials for this article are available online.
Keyword Empirical likelihood
Empirical process
Exponential tilting
Semiparametric model
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status Non-UQ
Additional Notes Accepted author version posted online: 25 Jul 2013

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Non HERDC
 
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Created: Fri, 21 Mar 2014, 02:26:30 EST by Kay Mackie on behalf of School of Mathematics & Physics