Variable Kernel Density Estimation

We investigate some of the possibilities for improvement of univariate and multivariate kernel density estimates by varying the window over the domain of estimation, pointwise and globally. Two general approaches are to vary the window width by the point of estimation and by point of the sample observation. The first possibility is shown to be of little efficacy in one variable. In particular, nearest-neighbor estimators in all versions perform poorly in one and two dimensions, but begin to be useful in three or more variables. The second possibility is more promising. We give some general properties and then focus on the popular Abramson estimator. We show that in many practical situations, such as normal data, a nonlocality phenomenon limits the commonly applied version of the Abramson estimator to bias of $O(\lbrack h / \log h\rbrack^2)$ instead of the hoped for $O(h^4)$ .We investigate some of the possibilities for improvement of univariate and multivariate kernel density estimates by varying the window over the domain of estimation, pointwise and globally. Two general approaches are to vary the window width by the point of estimation and by point of the sample observation. The first possibility is shown to be of little efficacy in one variable. In particular, nearest-neighbor estimators in all versions perform poorly in one and two dimensions, but begin to be useful in three or more variables. The second possibility is more promising. We give some general properties and then focus on the popular Abramson estimator. We show that in many practical situations, such as normal data, a nonlocality phenomenon limits the commonly applied version of the Abramson estimator to bias of $O(\lbrack h / \log h\rbrack^2)$ instead of the hoped for $O(h^4)$.

摘要来源：OpenAlex 索引摘要（稿件版本未注明）

笔记与分组

分类依据与纠错

Variable Kernel Density Estimation

代码、数据与补充材料

可变带宽核密度估计

原文摘要

同方向的基础文献

同方向的基础文献