Spline Regression in the Presence of Categorical Predictors
提出一种结合回归样条全局性质和分类核函数局部性质的新估计方法，处理同时包含连续和分类预测变量的非参数回归问题，相比传统方法有更好的有限样本表现。
Summary We consider the problem of estimating a relationship nonparametrically using regression splines when there exist both continuous and categorical predictors. We combine the global properties of regression splines with the local properties of categorical kernel functions to handle the presence of categorical predictors rather than resorting to sample splitting as is typically done to accommodate their presence. The resulting estimator possesses substantially better finite‐sample performance than either its frequency‐based peer or cross‐validated local linear kernel regression or even additive regression splines (when additivity does not hold). Theoretical underpinnings are provided and Monte Carlo simulations are undertaken to assess finite‐sample behavior; and two illustrative applications are provided. An implementation in R is available; see the R package ‘crs’ for details. Copyright © 2014 John Wiley & Sons, Ltd.