Mathematical Sciences: Smoothing Parameter Selection and Related Topic

数学科学：平滑参数选择及相关主题

• 批准号: 9205687
• 负责人: Shean-Tsong Chiu
• 金额: $ 11.1万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-01 至 1996-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9205687&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Smoothing; Parameter; Selection

The statistical part of this project will be to study a number of estimation methods using nonparametric approaches. In particular kernel estimation and related areas of nonparametric and density estimation applications will be studied, and the smoothing parameter selection problem addressed. Problems to be considered include those of discontinuities or rough density functions, selection for ridge regression, and the effect of discretization. The modelling part of this project involves new developments of the theory and applications of Markov models in both discrete and continuous time. The investigator will concentrate on rates of convergence results and on state and history dependent criteria for such stability. These results will be incorporated into a new approach to Markov decisions processes where the state space is extended to include the decision set into the overall Markovian structure. Stability properties of such general processes will then be established in quite complex environments. Probabilistic modelling and statistical estimation techniques encompass two separate parts of the same activity. The first part endeavors to describe, in manageable terms, models of real and often complex systems in such a way that the inherent randomness in the system is properly represented. The second endeavors to use these models, and data gathered to describe real systems, in such a way that one can estimate the parameters that actually describe what is happening in practice. In the modelling part of this project the investigators will study important models in operations research, time series, and finance and economics, with a focus on developing methods for stability of such systems. In the statistics part of the proposal, the investigators will look at a number of computer intensive ways of estimating parameters with a goal of finding methods which give good estimates quickly.

该项目的统计部分将研究一个 使用非参数方法的估计方法的数量。 在 特殊核估计及非参数相关领域 和密度估计的应用将进行研究， 解决了平滑参数选择问题。 问题需要 考虑包括那些不连续或粗糙密度 函数、岭回归的选择以及 离散化 该项目的建模部分涉及新的 马尔可夫模型的理论和应用的发展， 离散时间和连续时间。 研究者将 专注于收敛结果的速度和状态， 这种稳定性的历史依赖性标准。 这些结果 将被纳入马尔可夫决策的新方法中 扩展状态空间以包括 将决策集放入整体马尔可夫结构中。稳定性 这些一般过程的性质将建立在 非常复杂的环境。 概率建模和统计估计 技术包括同一活动的两个独立部分。 第一部分试图用可管理的术语描述模型 真实的和通常复杂的系统， 系统中的随机性被适当地表示。 第二 努力使用这些模型和收集的数据来描述真实的 系统，以这种方式，人们可以估计参数， 实际上描述了在实践中发生的事情。 在 研究人员将研究该项目的一部分 运筹学、时间序列和金融中的重要模型 和经济学，重点是发展稳定的方法 这样的系统。 在提案的统计部分， 调查人员将研究一些计算机密集型的方法， 估计参数的目标是找到方法， 快速准确的估计。