Kernel estimation of density level sets
Kernel estimation of density level sets
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DOI：
10.1016/j.jmva.2005.05.004
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发表时间：
2006-04-01
影响因子：
1.6
通讯作者：
Cadre, B
中科院分区：
文献类型：
--
作者：
Cadre, B
设f是多元密度，f(N)是取自n样本X-1的核估计，…身份证号码为X-N。密度为f的随机变量我们计算了t水平集f>；=i}和它的插件估计{f(N)>；=t}之间对称差的体积的渐近收敛速度。作为推论，我们得到了密度水平集的插入型估计的精确收敛速度，该估计对应于由f(C)2005 Elsevier Inc.导出的定律的固定概率。
Let f be a multivariate density and f(n) be a kernel estimate of f drawn from the n-sample X-1,... X-n of i.i.d. random variables with density f We compute the asymptotic rate of convergence towards 0 of the volume of the symmetric difference between the t-level set if >= i} and its plug-in estimator {f(n) >= t}. As a corollary, we obtain the exact rate of convergence of a plug-in-type estimate of the density level set corresponding to a fixed probability for the law induced by f (C) 2005 Elsevier Inc. All rights reserved.