Regression and Deconvolution with Heteroscedastic Measurement Error

异方差测量误差的回归和反卷积

• 批准号: 0304900
• 负责人: Leonard Stefanski
• 金额: $ 21.77万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-15 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0304900&HistoricalAwards=false
• 关键词: Regression; Deconvolution; Heteroscedastic; Measurement; Error

In the first component of the research, "Unbiased Estimation and Corrected-Score Methods for Heteroscedastic Measurement Error with Replicate Measurements," the investigator develops a general approach to statistical inference when data are measured with error. Starting with the assumptions that a valid statistical estimation method is known for error-free data, and that replicate measurements are made of the error-prone variate, the investigator shows how to modify the usual estimation method to eliminate bias induced by measurement error. The key technical advances include the accommodation of heteroscedastic measurement errors and replicate measurements, as well as development of a new Monte Carlo method of unbiased estimation of a normal mean. The author applies the general approach to m-estimation and density estimation, thereby incorporating a broad scope of statistical inference problems. In the second component of the research, "Deconvolution with Auxiliary Data," the investigator explores approaches to the deconvolution problem that exploit auxiliary variables correlated to the variable measured with error. The auxiliary variables play a roll akin to that of instrumental variables and are used to reduce variability in the deconvolution estimates.The astronomer's measurements of distances to galaxies, the epidemiologist's measurements of subjects' blood pressures, the environmental scientist's measurements of daily air pollution levels, and the sociologist's measurements of subjects' behaviors and attitudes share in common the fact that all are less than perfectly accurate. Measurement error is a pervasive problem in the analysis and interpretation of data that crosses disciplinary boundaries. It is a source of uncertainty that can bias estimates derived from data and lead to erroneous inferences. In this project the investigator develops theory and methods for statistical inference when data are measured with error. The research provides a new solution to a long-standing problem in statistical inference, and uses that solution to provide a comprehensive approach to the analysis of data measured with error. The primary benefit is improved statistical inference in the form of less biased and more accurate estimates calculated from scientific data. Because the prevalence of data measured with error is widespread, the impact of the research will be similarly widespread, finding immediate applications not only to the scientific fields mentioned above, but numerous others as well.

在研究的第一个组成部分，“无偏估计和校正分数方法异方差测量误差与重复测量，”研究人员开发了一种通用的方法来统计推断时，数据测量误差。假设一个有效的统计估计方法是已知的无误差的数据，重复测量的误差倾向的变量，调查显示如何修改通常的估计方法，以消除偏差引起的测量误差。关键的技术进步包括适应异方差测量误差和重复测量，以及发展一种新的蒙特卡罗方法的无偏估计的正态均值。作者适用于一般的方法m-估计和密度估计，从而纳入了广泛的统计推断问题。在研究的第二部分，“用辅助数据反卷积”，研究人员探讨了利用与误差测量变量相关的辅助变量的反卷积问题的方法。辅助变量的作用类似于工具变量，用于减少反卷积估计的可变性。天文学家测量到星系的距离，流行病学家测量受试者的血压，环境科学家测量每天的空气污染水平，社会学家对受试者行为和态度的测量有一个共同点，那就是所有的测量都不完全准确。测量误差是跨学科数据分析和解释中的一个普遍问题。它是一个不确定性的来源，可能会使从数据中得出的估计产生偏差，并导致错误的推断。在这个项目中，研究人员开发的理论和方法的统计推断时，数据测量误差。该研究为统计推断中的一个长期存在的问题提供了一种新的解决方案，并使用该解决方案提供了一种全面的方法来分析有误差的测量数据。主要好处是改进统计推断，根据科学数据计算出的估计偏差更小、更准确。由于带有误差的测量数据的普遍性是普遍存在的，因此研究的影响也将同样广泛，不仅可以立即应用于上述科学领域，还可以应用于许多其他领域。