核密度函數估計量之偏量性質的改善方法

Bias Reduction for Kernel Density Estimator

鄭真卿(Chen-Chin Cheng)

指導教授 ： 鄧文舜

淡江大學/商管學院/統計學系應用統計學碩士班/碩士(2020年)

https://doi.org/10.6846/TKU.2020.00282

摘要

本研究探討核密度函數估計量之偏量性質的改善方法, 分成六個章節；第一章導論, 描述在估計母體密度函數f的無母數方法中, 使用核密度函數估計量的優點；第二章提岀改良式核密度函數估計量f ̂_D；第三章為探究改良式核密度函數估計量之理論性質；第四章針對兩筆實際資料, 分別是紐約州水牛城1910-1972一共62年的降雪量資料, 以及320位男性胸痛病人血漿總膽固醇濃度資料, 以改良式核密度函數估計量進行密度函數估計；第五章為模擬研究, 針對改良式核密度函數估計量f ̂_D進行一系列基於模擬資料的研究, 並與傳統f ̂ 做比較；第六章為本研究結論；第七章為理論證明。

關鍵字

期望積分均方差 ； 積分變異數 ； 積分平方偏量 ； 帶寬值

並列摘要

Kernel density estimator is a nonparametric method to recover the true probability density functions, It is a useful nonprametric smoothing method as it uses no assumption about the true probability function. Unfortunately, optimal efficient kernel density estimators are biased which hinders the development of methods for further statistical inference. In this dissertation, we apply the method of Cheng et al. (2018), which serves to reduce the bias of kernel regression function estimator, to reduce the bias of classical kernel density estimates. The proposed method does not inflate the variance. It needs not to use higher-order kernel function whose theoretical advantages do not transfer to reasonably sized samples. The theoretical properties of the proposed estimator are provided two real-data applications are demonstrated. Simulations are carried out for comparisons with regular kernel density estimator. The results reveals that the biased corrected kernel density estimator enjoys noticeably smaller mean integrated square errors.

並列關鍵字

mean integrated squared error ； integrated variance ； integrated square bias ； bandwidth

參考文獻

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