Abstract We propose kernel-based estimators for both the parametric and nonparametric components of a partially linear additive regression model where a subset of the covariates entering the nonparametric component are generated by the estimation of an auxiliary nonparametric regression. Both estimators are shown to be asymptotically normally distributed. The estimator for the finite dimensional parameter is shown to converge at the parametric n rate and the estimator for the infinite dimensional parameter converges at a slower nonparametric rate that, as usual, depends on the rate of decay of the bandwidths and the dimensionality of the underlying regression. A small Monte Carlo study is conducted to shed light on the finite sample performance of our estimators and to contrast them with those of estimators available in the extant literature.

中文翻译：

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具有生成协变量的部分线性加性模型的估计

摘要 我们为部分线性加性回归模型的参数和非参数分量提出了基于内核的估计器，其中进入非参数分量的协变量子集是通过辅助非参数回归的估计生成的。两个估计量都显示为渐近正态分布。有限维参数的估计以参数 n 速率收敛，无限维参数的估计以较慢的非参数速率收敛，通常取决于带宽的衰减速率和底层的维数回归。进行了一项小型 Monte Carlo 研究，以阐明我们的估计器的有限样本性能，并将它们与现有文献中可用的估计器的性能进行对比。