Propagation-separation approach for local likelihood estimation
Propagation-separation approach for local likelihood estimation
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DOI：
10.1007/s00440-005-0464-1
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发表时间：
2006-07-01
影响因子：
2
通讯作者：
Spokoiny, V
中科院分区：
文献类型：
--
作者：
Polzehl, J;Spokoiny, V
本文提出了一个统一的方法来局部似然估计的广泛的一类非参数模型，包括例如回归，密度，泊松和二进制响应模型。该方法扩展了Polzehl和Spokoiny（2000）在图像去噪背景下引入的自适应权重平滑（AWS）过程。该方法的主要思想是描述每个设计点X-i的最大可能局部邻域，其中局部参数假设由数据证明。该方法是特别强大的模型功能具有大的均匀区域和尖锐的不连续性。所提出的方法的性能示出了密度估计和分类的数值例子。我们还建立了一些显着的理论非渐近性质的新算法的结果。这包括“传播”属性，特别是在齐次情况下产生的估计的根n一致性。我们还陈述了一个“预言”结果，这意味着在通常的光滑条件下估计的速率最优性和一个“分离”结果，这解释了该方法对结构变化的敏感性。
The paper presents a unified approach to local likelihood estimation for a broad class of nonparametric models, including e.g. the regression, density, Poisson and binary response model. The method extends the adaptive weights smoothing (AWS) procedure introduced in Polzehl and Spokoiny (2000) in context of image denoising. The main idea of the method is to describe a greatest possible local neighborhood of every design point X-i in which the local parametric assumption is justified by the data. The method is especially powerful for model functions having large homogeneous regions and sharp discontinuities. The performance of the proposed procedure is illustrated by numerical examples for density estimation and classification. We also establish some remarkable theoretical nonasymptotic results on properties of the new algorithm. This includes the "propagation'' property which particularly yields the root-n consistency of the resulting estimate in the homogeneous case. We also state an "oracle" result which implies rate optimality of the estimate under usual smoothness conditions and a "separation'' result which explains the sensitivity of the method to structural changes.