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摘要翻译：
本文提出了一种新的空间自适应局部（常数）似然估计方法，该方法适用于一类广泛的非参数模型，包括高斯模型、泊松模型和二元响应模型。该方法的主要思想是，在给定一系列局部似然估计（弱估计）的情况下，构造一个新的集合估计，其点态风险是所有弱估计中风险最小的一阶。我们还提出了一种新的方法来选择过程的参数，通过提供所得到的估计在简单参数情况下的规定行为。我们建立了关于集合估计最优性的一些重要的理论结果。特别是，我们的“甲骨文”结果声称，它的风险是，直到某个对数乘数，等于给定估计族的最小风险。通过对分类问题的应用，说明了该方法的性能。数值模拟和实际算例表明了该方法的合理性能。
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英文标题：
《Spatial aggregation of local likelihood estimates with applications to
classification》
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作者：
Denis Belomestny, Vladimir Spokoiny
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
This paper presents a new method for spatially adaptive local (constant) likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of the method is, given a sequence of local likelihood estimates (``weak'' estimates), to construct a new aggregated estimate whose pointwise risk is of order of the smallest risk among all ``weak'' estimates. We also propose a new approach toward selecting the parameters of the procedure by providing the prescribed behavior of the resulting estimate in the simple parametric situation. We establish a number of important theoretical results concerning the optimality of the aggregated estimate. In particular, our ``oracle'' result claims that its risk is, up to some logarithmic multiplier, equal to the smallest risk for the given family of estimates. The performance of the procedure is illustrated by application to the classification problem. A numerical study demonstrates its reasonable performance in simulated and real-life examples.
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PDF链接：
https://arxiv.org/pdf/712.0939
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