  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.
