Semiparametric inference of grouped zero-inflated poisson models

doi:10.7523/j.issn.2095-6134.2009.2.005

›› 2009, Vol. 26 ›› Issue (2): 173-184.DOI: 10.7523/j.issn.2095-6134.2009.2.005

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Semiparametric inference of grouped zero-inflated poisson models

ZHONG Yu-Ke¹, XUE Hong-Qi², ZHANG San-Guo¹

1. School of Mathematical Sciences, Graduate University of the Chinese Academy of Sciences, Beijing 100049, China;
2. Department of Biostatistics and Computational Biology, University of Rochester, U.S.A.

Received:2008-05-15 Revised:2008-09-03 Online:2009-03-15

Abstract

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

CLC Number:

O213

ZHONG Yu-Ke, XUE Hong-Qi, ZHANG San-Guo. Semiparametric inference of grouped zero-inflated poisson models[J]. , 2009, 26(2): 173-184.

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Semiparametric inference of grouped zero-inflated poisson models

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