Bayesian Inference Estimation in Nonparametric Regression and its Frequentist Properties

非参数回归中的贝叶斯推理估计及其频率属性

• 批准号: 9971848
• 负责人: Linda Zhao
• 金额: --
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-15 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971848&HistoricalAwards=false
• 关键词: Bayesian; Inference; Estimation; Nonparametric; Regression

Nonparametric regression analysis is a rapidly developing contemporary statistical methodology. It avoids some of the restrictive assumptions in more classical regression approaches. However, to date it has suffered by comparison from an almost total absence of the inferential tools (e.g. tests and confidence intervals) which help make classical regression analysis so useful. Zhao (1998 preprint) proposed the first proper Bayesian estimator for nonparametric regression which has acceptable performance for every sample size. The current proposal is to extend this construction in various ways and to study the inferential properties related to such Bayesian formulations. Its various properties, including the acceptable performance of its Bayes estimator, suggest that Bayesian inference based on this prior distribution and its extensions may be feasible. They may also present a satisfactory comprehensive set of inferential tools for nonparametric regression analysis and related formulations.Regression analysis is a classical general statistical tool, which has been widely used in virtually every area of statistical applications. Nonparametric regression analysis is a more recent methodology, which avoids some restrictive assumptions in the classical theory. The general theory includes nonparametric formulations of regression, of density estimation, of signal processing and of spectral density estimation in time series analysis. The theory has already found significant applications in areas such as medical and environmental imaging, economic analysis, computer engineering, and geophysics. Bayesian analysis is a very powerful general statistical methodology. This research project proposes a possible way of using Bayesian techniques to solve nonparametric regression problems.

非参数回归分析是一种快速发展的当代统计方法。 它避免了更经典的回归方法中的一些限制性假设。 然而，迄今为止，由于几乎完全缺乏推理工具（例如测试和置信区间），这使得经典回归分析变得如此有用。 赵（1998 年预印本）提出了第一个适用于非参数回归的贝叶斯估计器，它对于每个样本大小都具有可接受的性能。 目前的建议是以各种方式扩展这种构造，并研究与此类贝叶斯公式相关的推理属性。 它的各种属性，包括其贝叶斯估计器的可接受的性能，表明基于此先验分布及其扩展的贝叶斯推理可能是可行的。 它们还可以为非参数回归分析和相关公式提供一套令人满意的综合推理工具。回归分析是一种经典的通用统计工具，几乎已广泛应用于统计应用的每个领域。 非参数回归分析是一种较新的方法，它避免了经典理论中的一些限制性假设。 一般理论包括时间序列分析中回归、密度估计、信号处理和谱密度估计的非参数公式。该理论已经在医学和环境成像、经济分析、计算机工程和地球物理学等领域找到了重要的应用。 贝叶斯分析是一种非常强大的通用统计方法。 该研究项目提出了一种使用贝叶斯技术解决非参数回归问题的可能方法。