He Xuming, Xue Hongqi, Shi Ning-Zhong
Department of Statistics, University of Illinois at Urbana-Champaign, Department of Biostatistics and Computational Biology, University of Rochester, School of Mathematics and Statistics, Northeast Normal University, China.
J Multivar Anal. 2010 Oct;101(9):2026-2038. doi: 10.1016/j.jmva.2010.05.003.
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.
对于诸如收入或病假天数等非负测量值，零计数往往具有特殊地位。此外，零计数的发生率通常高于泊松模型的预期。本文考虑一种双重半参数零膨胀泊松模型来拟合此类数据，该模型在泊松分量的均值和零概率中都假设了两个部分线性链接函数。我们研究了回归参数和非参数函数的筛极大似然估计量。我们表明，在常规条件下，估计量是强一致的。此外，参数估计量是渐近正态且一阶有效的，而非参数分量达到了最优收敛速度。模拟研究表明，双重半参数模型固有的额外灵活性在统计效率上几乎没有损失。我们还用一项公共卫生研究的数据集说明了我们的方法。
