Comparing two samples by penalized logistic regression

Details Comparing two samples by penalized logistic regression Comparing two samples by penalized logistic regression

2008-07-16

arxiv.org/abs/0807.2563v1

Electronic Journal of Statistics 2008, Vol. 2, 564-580

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-EJS078 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

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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