Smoothing Bias in Density Derivative Estimation
研究了局部平滑密度估计中导数估计的系统性向下偏差，分析了核估计量的偏差来源，并针对得分向量提出比例偏差近似和诊断统计量，对从事非参数估计和回归模型自适应估计的研究者有参考价值。
Abstract This article discusses a generic feature of density estimation by local smoothing, namely that estimated derivatives and location score vectors will display a systematic downward (attenuation) bias. We study the behavior of kernel estimators, indicating how the derivative bias arises and showing a simple result. We then consider the estimation of score vectors (negative log-density derivatives), which are motivated by the problem of estimating average derivatives and the adaptive estimation of regression models. Using “fixed bandwidth” limits, we show how scores are proportionally downward biased for normal densities and argue from normal mixture densities that proportional bias can be a reasonable approximation. We propose a simple diagnostic statistic for score bias.