The local kernel pseudo-partial likelihood is employed for estimation in a panel count model with nonparametric covariate functions. An estimator of the derivative of the nonparametric covariate function is derived first, and the nonparametric function estimator is then obtained by integrating the derivative estimator. Uniform consistency rates and pointwise asymptotic normality are obtained for the local derivative estimator under some regularity conditions. Moreover, the baseline function estimator is shown to be uniformly consistent. Demonstration of the asymptotic results strongly relies on the modern empirical theory, which generally does not require the Poisson assumption. Simulation studies also illustrate that the local derivative estimator performs well in a finite-sample regardless of whether the Poisson assumption holds. We also implement the proposed methodology to analyze a clinical study on childhood wheezing.

中文翻译：

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具有非参数协变量函数的面板计数数据的核回归模型

局部核伪偏似然用于具有非参数协变量函数的面板计数模型中的估计。首先导出非参数协变量函数的导数估计量，然后通过对导数估计量进行积分得到非参数函数估计量。局部导数估计量在一定的正则性条件下得到了一致的一致性率和逐点渐近正态性。此外，基线函数估计器被证明是一致的。渐近结果的证明强烈依赖于现代经验理论，一般不需要泊松假设。模拟研究还表明，无论泊松假设是否成立，局部导数估计器在有限样本中的表现都很好。