Near-Linear Time Local Polynomial Nonparametric Estimation with Box Kernels
Warrington College of Business, University of Florida（佛罗里达大学沃顿商学院）；Institute of Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Paul G. Allen School of Computer Science and Engineering, University of Washington（华盛顿大学保罗·G·艾伦计算机科学与工程学院）
英文摘要：
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this paper, we significantly accelerate the computation of local polynomial estimates by novel applications of multi-dimensional binary indexed trees (Fenwick 1994). Both time and space complexity of our proposed algorithm is nearly linear in the number of input data points. Simulation results confirm the efficiency and effectiveness of our proposed approach.
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