A minimum relative entropy based correlation model between the response and covariates

Summary A semiparametric model is presented utilizing dependence between a response and several covariates. We show that this model is optimum when the marginal distributions of the response and the covariates are known. This model extends the generalized linear model and the proportional likelihood ratio model when the marginal distributions are unknown. New interpretations of known models such as the logistic regression model, density ratio model and selection bias model are obtained in terms of dependence between variables. For estimation of parameters, a simple algorithm is presented which is guaranteed to converge. It is also the same regardless of the choice of the distribution for response and covariates; hence, it can fit a very wide variety of useful models. Asymptotic properties of the estimators of model parameters are derived. Real data examples are discussed to illustrate our approach and simulation experiments are performed to compare with existing procedures.