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Sieve maximum likelihood estimation for doubly semiparametric zero-inflated Poisson models

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  • He, Xuming
  • Xue, Hongqi
  • Shi, Ning-Zhong

Abstract

For 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.

Suggested Citation

  • He, Xuming & Xue, Hongqi & Shi, Ning-Zhong, 2010. "Sieve maximum likelihood estimation for doubly semiparametric zero-inflated Poisson models," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2026-2038, October.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:9:p:2026-2038
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    References listed on IDEAS

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    1. 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.
    2. 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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    4. Xue H. & Lam K.F. & Li G., 2004. "Sieve Maximum Likelihood Estimator for Semiparametric Regression Models With Current Status Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 346-356, January.
    5. K. F. Lam & Hongqi Xue & Yin Bun Cheung, 2006. "Semiparametric Analysis of Zero-Inflated Count Data," Biometrics, The International Biometric Society, vol. 62(4), pages 996-1003, December.
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    Cited by:

    1. Nadja Klein & Thomas Kneib & Stefan Lang, 2015. "Bayesian Generalized Additive Models for Location, Scale, and Shape for Zero-Inflated and Overdispersed Count Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 405-419, March.
    2. Das, Ujjwal & Das, Kalyan, 2018. "Inference on zero inflated ordinal models with semiparametric link," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 104-115.
    3. Lamarche, Carlos & Shi, Xuan & Young, Derek S., 2024. "Conditional Quantile Functions for Zero-Inflated Longitudinal Count Data," Econometrics and Statistics, Elsevier, vol. 31(C), pages 49-65.

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