Sieve maximum likelihood estimation for doubly semiparametric zero-inflated Poisson models
AbstractFor nonnegative measurements such as income or sick days, zero counts often have special status. Furthermore, the incidence of zero counts is often greater than expected for the Poisson model. This article considers a doubly semiparametric zero-inflated Poisson model to fit data of this type, which assumes two partially linear link functions in both the mean of the Poisson component and the probability of zero. We study a sieve maximum likelihood estimator for both the regression parameters and the nonparametric functions. We show, under routine conditions, that the estimators are strongly consistent. Moreover, the parameter estimators are asymptotically normal and first order efficient, while the nonparametric components achieve the optimal convergence rates. Simulation studies suggest that the extra flexibility inherent from the doubly semiparametric model is gained with little loss in statistical efficiency. We also illustrate our approach with a dataset from a public health study.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 101 (2010)
Issue (Month): 9 (October)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Li, Chin-Shang & Taylor, Jeremy M. G. & Sy, Judy P., 2001. "Identifiability of cure models," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 389-395, October.
- Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
- Jansakul, N. & Hinde, J. P., 2002. "Score Tests for Zero-Inflated Poisson Models," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 75-96, July.
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