A variable bandwidth selector in multivariate kernel density estimation
A variable bandwidth selector in multivariate kernel density estimation
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DOI：
10.1016/j.spl.2006.08.013
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发表时间：
2007-02-15
影响因子：
0.8
通讯作者：
Chen, Huang-Yu
中科院分区：
文献类型：
--
作者：
Wu, Tiee-Jian;Chen, Ching-Fu;Chen, Huang-Yu
基于未知d维密度函数f的随机样本，研究了f的核估计中可变（或自适应）带宽的选择问题.常用的策略是将每个观测的可变带宽表示为局部带宽因子和全局平滑参数的乘积。提出了一种基于聚类分析的局部带宽因子选取方法。这种方法是直接和直观的吸引力。为了选择全局平滑参数，一种方法是在Wu和Tsai [2004]中选择固定带宽的频域方法的适应。多元核密度估计中的根n带宽选择器。可能吧理论相关领域129，537-558]。对于d = 1和2，已经进行了广泛的模拟研究，以比较我们的选择器与Abramson [1982.核估计中的带宽变化-平方根定律。安。统计员。10，1217-1223]以及Sain和Scott [1996.油局部自适应密度估计。J. Amer.国家主义者。Assoc.91，1525-1534]和Sain [2002.多变量局部自适应密度估计。Comput.中央集权主义者数据分析39 165-186]，我们的选择器在实际样本量下的出色性能得到了清楚的证明。(c)2006 Elsevier B. V.保留所有权利。
Based on a random sample of size n from an unknown d-dimensional density f, the problem of selecting the variable (or adaptive) bandwidth in kernel estimation of f is investigated. The common strategy is to express the variable bandwidth at each observation as the product of a local bandwidth factor and a global smoothing parameter. For selecting the local bandwidth factor a method based on cluster analysis is proposed. This method is direct and intuitively appealing. For selecting the global smoothing parameter a method that is an adaptation of the frequency domain approach of selecting the fixed bandwidth in Wu and Tsai [2004. Root n bandwidths selectors in multivariate kernel density estimation. Probab. Theory Related Fields 129, 537-558] is used. For d = 1 and 2, extensive simulation studies have been done to compare the performance of our selector with the selectors of Abramson [1982. Oil bandwidth variation in kernel estimates-a square root law. Ann. Statist. 10, 1217-1223] and Sain and Scott [1996. Oil locally adaptive density estimation. J. Amer. Statist. Assoc. 91, 1525-1534] and Sain [2002. Multivariate locally adaptive density estimation. Comput. Statist. Data Anal. 39 165-186], and the excellent performance of our selector at practical sample sizes is clearly demonstrated. (c) 2006 Elsevier B.V. All rights reserved.