一种脊参数反褶积方法

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摘要翻译：
核方法的反卷积具有吸引人的特点，并在文献中盛行。然而，它们也有缺点，包括它们通常只适用于误差分布无限支持且其特征函数永远不会消失的情况。即使在这些情况下，只有当核的选择适应于目标分布的未知光滑性时，核估计才能获得最优的收敛速度。在本文中，我们提出了替代脊方法，不涉及核任何方式。我们证明了岭方法(a)不要求误差分布特征函数为非消失的假设；(b)对目标密度的平滑度适应得非常好，其结果是平滑度不需要直接估计；和(c)给出在广泛的设置范围内的最佳收敛速度。
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英文标题：
《A ridge-parameter approach to deconvolution》
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作者：
Peter Hall, Alexander Meister
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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：
  Kernel methods for deconvolution have attractive features, and prevail in the literature. However, they have disadvantages, which include the fact that they are usually suitable only for cases where the error distribution is infinitely supported and its characteristic function does not ever vanish. Even in these settings, optimal convergence rates are achieved by kernel estimators only when the kernel is chosen to adapt to the unknown smoothness of the target distribution. In this paper we suggest alternative ridge methods, not involving kernels in any way. We show that ridge methods (a) do not require the assumption that the error-distribution characteristic function is nonvanishing; (b) adapt themselves remarkably well to the smoothness of the target density, with the result that the degree of smoothness does not need to be directly estimated; and (c) give optimal convergence rates in a broad range of settings.
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PDF链接：
https://arxiv.org/pdf/710.3491

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关键词：distribution disadvantage Multivariate convolution Convergence error kernel characteristic 光滑性 convergence