关键词: 零膨胀泊松回归模型, 部分线性模型, Sieve极大似然估计, 强相合, 渐近有效

Abstract:

The incidence of zero counts is often greater than expected for the Poisson distribution and zero counts frequently have special status. And sometimes the count data may be grouped, which means that for some observation the count is not known exactly but is known to fall in a particular range. This paper considers a semiparametric zero-inflated Poisson (ZIP) model to fit such grouped data with excess zeros, where the partial linear link function is used in the mean of the Poisson distribution and the linear link function is used in modeling the probability of zero. A Sieve maximum likelihood estimator(MLE) is proposed to estimate both the regression parameters and the nonparametric function, and a score test is provided for the presence of excess zeros. Asymptotic properties of the proposed Sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strong consistent. Moreover, the estimators of the unknown parameters are asymptotic efficient and normally distributed. The estimator of the nonparametric function has optimal convergence rate. Simulation studies are carried out to investigate the performance of the proposed method. For illustration purpose, the method is applied to a data set from a public health survey.

Key words: zero-inflated Poisson model, partial linear models, Sieve maximum likelihood estimator, strongly consistent, asymptotically efficient