Open Access
2008 Comparing two samples by penalized logistic regression
Konstantinos Fokianos
Electron. J. Statist. 2: 564-580 (2008). DOI: 10.1214/07-EJS078


Inference based on the penalized density ratio model is proposed and studied. The model under consideration is specified by assuming that the log–likelihood function of two unknown densities is of some parametric form. The model has been extended to cover multiple samples problems while its theoretical properties have been investigated using large sample theory. A main application of the density ratio model is testing whether two, or more, distributions are equal. We extend these results by arguing that the penalized maximum empirical likelihood estimator has less mean square error than that of the ordinary maximum likelihood estimator, especially for small samples. In fact, penalization resolves any existence problems of estimators and a modified Wald type test statistic can be employed for testing equality of the two distributions. A limited simulation study supports further the theory.


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Konstantinos Fokianos. "Comparing two samples by penalized logistic regression." Electron. J. Statist. 2 564 - 580, 2008.


Published: 2008
First available in Project Euclid: 16 July 2008

zbMATH: 1320.62070
MathSciNet: MR2426102
Digital Object Identifier: 10.1214/07-EJS078

Primary: 62G05
Secondary: 62G20

Keywords: Biased sampling , empirical likelihood , Mean square error , Penalty , power , semiparametric , shrinkage

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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