Optimal Curve Estimation: from Asymptotic to Small Sample Sizes

最优曲线估计：从渐近到小样本量

• 批准号: 9971051
• 负责人: Sam Efromovich
• 金额: $ 5.1万
• 依托单位: University of New Mexico
• 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: 1999-09-01 至 2002-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971051&HistoricalAwards=false
• 关键词: Optimal; Curve; Estimation; Asymptotic; Small

SAM EFROMOVICH Optimal curve estimation: from asymptotic to small sample sizes9971051The primary focus of this research is to explore the bridges between the sharp asymptotic theory of nonparametric curve estimation and practically important cases of small sample sizes. Main objectives are as follows: (i) For the case of classical direct statistical settings, like density estimation or heteroscedastic regression, create the theory and methods of finding minimal sample sizes (the degree of the problem) where asymptotically sharp data-driven estimates outperform any other estimates. (ii) For indirect statistical problems, such as nonparametric survival analysis, blurred images or regressionwith measurement errors in predictors, create the theory of equivalence between these settings and the corresponding direct ones with a particular emphasis on finding the relation between sample sizes needed for a similar quality of estimation. (iii) For nonparametric curve estimation problems involving time series with heavy tails and long range dependence, which frequently arise in the modern communication systems like the World Wide Web, develop optimal data-driven procedures of nonparametric estimation. Statistical theory is primarily interested in finding most accurate procedures for large samples while in practically interesting cases sample sizes may be both large and small. Moreover, the notion of a large or small sample depends on an underlying setting. The research is devoted to developing universal procedures, which are simultaneously optimal for both large and small sample sizes. The developed methods will be tested on the following specific practical problems which motivated this proposal: (1) Insulin secretion by the type II diabetes patients; (2) The geomagnetic polarity time-scale and the speed of seafloor spreading using marine magnetic observations, and how these factors affect environment and global change; (3) Drinking water quality including monitoring arsenic and other cancer-causing substances in New Mexico; (4) Learning machines for screening patients in emergency rooms; (5) Engineered systems for the analysis of transformed and noisy images. These applied problems will be done together with Sandia National Laboratories, the UNM Medical Center and Maui High Performance Computing Center.

SAM EFROMOVICH 最优曲线估计：从渐近到小样本量9971051本研究的主要重点是探索非参数曲线估计的尖锐渐近理论与小样本量的实际重要案例之间的桥梁。 主要目标如下：（i）对于经典直接统计设置的情况，如密度估计或异方差回归，创建寻找最小样本量（问题的程度）的理论和方法，其中渐近尖锐的数据驱动估计优于任何其他估计。 (ii) 对于间接统计问题，例如非参数生存分析、模糊图像或预测变量中存在测量误差的回归，创建这些设置与相应直接设置之间的等效理论，特别强调找到相似估计质量所需的样本量之间的关系。 (iii) 对于涉及重尾和长程依赖的时间序列的非参数曲线估计问题，这些问题在万维网等现代通信系统中经常出现，开发最佳的数据驱动的非参数估计程序。统计理论主要感兴趣的是为大样本找到最准确的程序，而在实际有趣的情况下，样本量可能既大又小。 此外，大样本或小样本的概念取决于基本设置。 该研究致力于开发通用程序，该程序对于大样本量和小样本量同时都是最佳的。 所开发的方法将针对以下具体实际问题进行测试，这些问题激发了该提案：（1）II型糖尿病患者的胰岛素分泌； (2) 利用海洋磁观测得出的地磁极性时间尺度和海底扩张速度，以及这些因素如何影响环境和全球变化； （3）饮用水质量，包括监测新墨西哥州的砷和其他致癌物质； (4) 急诊室病人筛查学习机； (5) 用于分析变换图像和噪声图像的工程系统。这些应用问题将与桑迪亚国家实验室、新墨西哥大学医学中心和毛伊岛高性能计算中心共同完成。