Semiparametric Weighting Estimations of a Zero-Inflated Poisson Regression with Missing in Covariates

We scrutinize the problem of missing covariates in the zero-inflated Poisson regression model. Under the assumption that some covariates for modeling the probability of the zero and the nonzero states are missing at random, the complete-case estimator is known to be biased and inefficient. Although the inverse probability weighting estimator is unbiased, it remains inefficient. We propose four types of semiparametric weighting estimations where the conditional probabilities and the conditional expected score functions are estimated either by using the generalized additive models (GAMs) and the Nadaraya kernel smoother method. In addition, we allow the conditional probabilities and the conditional expectations to be either of the same types or of different types. Moreover, a Monte Carlo experiment is used to investigate the merit of the proposed method.