轉換核密度函數估計法之邊界效應改善及偏差減小

Boundary Correction and Bias Reduction in Transformation Kernel Density Estimation

洪萬吉(Wann-Jyi Horng)

《大葉學報》 13卷1期 (2004/06) Pp. 17-22

https://doi.org/10.7119/JDYU.200406.0017

摘要

Ruppert與Cline [13] 提出轉換的核密度估計法，且使用它來估計未知密度函數。由於轉換的核密度估計量，在估計邊界區域時會造成所謂的邊界效果，本文提出利用Ruppert與Cline估計量與最小平方法結合之觀點，建立一個新的轉換的核密度估計量。所提之轉換的核密度估計量具有改善原Ruppert與Cline法之核估計量的缺點及不會產生估計值為負的優點。此外，所提之核估計量若結合在Ruppert與Cline [13] 之疊代法疊代j次，則偏差可達到O()，hj為第j((1) 次疊代之帶寬，另本文也將提供所提估計量之收斂速率及建立其近似分配為常態。

關鍵字

經驗分配轉換 ； 累積分配函數 ； 平滑參數 ； 偏差減小 ； 邊界效果

並列摘要

Ruppert and Cline [13] proposed the method of transformation-kernel density estimator, and used it to estimate the unknown density function. The transformation-kernel density estimator is known to have boundary effects. In this article, we propose a new transformation-kernel density estimator, which is a hybrid of the original Ruppert-Cline estimator and of the least squares method. The proposed method has the advantage of having positive resulting density estimator and it also improves upon the Ruppert-Cline method. Besides, when incorporated with the iterative method in Ruppert and Cline [13], the bias of the proposed estimator can achieve the order O(), where hj is the bandwidth used in the j-th iteration. In this article, we also derive the convergence rate and establish the asymptotic normality for the proposed estimator.

並列關鍵字

empirical distribution transformation ； cumulative distribution function ； smoothing parameter ； bias reduction ； boundary effects