Nonparametric regressions are powerful statistical tools that can be used to model relationships between dependent and independent variables with minimal assumptions on the underlying functional forms. Despite their potential benefits, these models have two weaknesses: The added flexibility creates a curse of dimensionality, and procedures available for model selection, like crossvalidation, have a high computational cost in samples with even moderate sizes. An alternative to fully nonparametric models is semiparametric models that combine the flexibility of nonparametric regressions with the structure of standard models. In this article, I describe the estimation of a particular type of semiparametric model known as the smooth varying-coefficient model (Hastie and Tibshirani, 1993, Journal of the Royal Statistical Society, Series B 55: 757–796), based on kernel regression methods, using a new set of commands within vc_pack. These commands aim to facilitate bandwidth selection and model estimation as well as create visualizations of the results.

非参数回归是功能强大的统计工具，可用于在基本功能形式的假设最少的情况下对因变量和自变量之间的关系进行建模。尽管它们具有潜在的好处，但它们具有两个缺点：增加的灵活性会造成维数的折磨，而用于模型选择的过程（如交叉验证）在大小适中的样本中具有很高的计算成本。完全非参数模型的替代方法是半参数模型，该模型将非参数回归的灵活性与标准模型的结构结合在一起。在本文中，我描述了一种特殊类型的半参数模型的估计，该模型称为平滑变化系数模型（Hastie和Tibshirani，1993，皇家统计学会杂志，系列B 55：757–796），基于内核回归方法，使用vc_pack中的一组新命令。这些命令旨在促进带宽选择和模型估计以及创建结果的可视化。