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中，“无偏估计和校正得分方法，用于通过重复测量进行异质的测量误差”，研究者在使用误差测量数据时开发了一种通用统计推断的方法。从假设有效的统计估计方法以无错误数据为已知的假设，并且重复测量是对易于错误的变量进行的，研究者展示了如何修改通常的估计方法以消除通过测量错误引起的偏差。关键的技术进步包括适应异性范围的测量误差和复制测量，以及开发一种新的蒙特卡洛方法，即对正常平均值进行无偏估计。作者将一般方法应用于M估计和密度估计，从而结合了广泛的统计推断问题。在研究的第二个组成部分中，“带有辅助数据的反卷积”，研究人员探索了利用辅助变量与与误差测量的变量相关的反卷积问题的方法。辅助变量的起作用类似于仪器变量的滚动，用于降低反卷积估计的变异性。天文学家对星系距离的距离的测量值，流行病学家对受试者的血液压力的测量，环境科学家对每日空气污染水平的衡量等级的衡量等等，以及对社会的衡量标准的衡量。而不是完全准确。在分析和解释跨学科边界的数据中，测量误差是一个普遍的问题。它是不确定性的来源，可以偏向于数据得出的估计并导致错误的推论。在该项目中，研究者在使用错误测量数据时开发了统计推断的理论和方法。该研究为统计推断中的长期存在问题提供了一种新的解决方案，并使用该解决方案为分析错误的数据提供了全面的方法。主要的好处是改善了从科学数据计算出的偏差和更准确估计的形式的统计推断。由于用误差测量的数据的流行率很普遍，因此研究的影响将同样广泛，不仅在上述科学领域，而且还有许多其他领域，还可以直接应用。