Generalized Partially Linear Single-index Models For Zero-inflated Count Data

The non-negative event count data arise in many modern scientific endeavor, however they often have the feature that excessive zeros happen in the observed numbers. The zero-inflated model provides a flexible way to account for this feature. This article sets foot on both asymptot-ic properties and practical sides of semiparametric zero-inflated Poisson models. A generalized partially linear single-index model is introduced for either the mean of the Poisson component or the probability of zeros, and a profile maximum likelihood estimator is proposed. Under some mild conditions, asymptotic properties of the profile likelihood estimator are established. The finite sample performance of the proposed method is demonstrated by the analyses of the article production data and the medical care real data.The contents of the paper is as follows. Section1describe some basic theory we need. Section2describes the semiparametric ZIP model and proposes the estimation procedure. The asymptotic properties of the estimator are studied. Section3provides a computation algorithm for solving the estimating functions and illustrates the estimation performance with Monte Carlo simulation results. Section4carries on the proposed method for two real datasets to illustrate the computational simplicity. Section5ends the paper with a brief discussion. All the technical proofs of the asymptotic results are deferred to the Appendix.