Mathematical Sciences: Self-Consistent Estimators, Bootstrap and Censored Data

数学科学：自洽估计、引导和审查数据

• 批准号: 9510376
• 负责人: Jian-Jian Ren
• 金额: $ 1.8万
• 依托单位: University of Nebraska-Lincoln
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-15 至 1997-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9510376&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Self; Consistent; Estimators

9510376 Ren Abstract The proposed research is concerned with the statistical inference problems using various types of censored data, including right censored, doubly censored, interval censored, left truncated - right censored, and bivariate censored data. Estimation, tests and confidence intervals with incomplete date are all under consideration. One objective of the research is to investigate a new resampling method, called the Leveraged Bootstrap, so that the difficulty of extending the usual estimation and testing procedures for complete data to incomplete data in certain situations or certain complicated models can be avoided. So far, the procedures developed for incomplete data are constructed on an ad hoc basis. The leveraged bootstrap does not rely on these ad hoc extensions. The research will focus on the investigation of the consistency of the leveraged bootstrap in a number of important statistical inference problems with incomplete data, such as empirical likelihood inference, nonparametric likelihood confidence bands, linear regression models, tests of independence for two random variables, tests in some semiparametric change point models, mixture models and biased sampling problems. Another objective of the research is to investigate the consistency of the m out of n bootstrap, i.e., resampling fewer than n observations, in the hypothesis testing problems using various censored data. It is known that the usual nonparametric bootstrap (the n out of n bootstrap) fails when one tries to estimate the distribution of test statistics under a semiparametric (restricted nonparametric) hypothesis and ignores the restrictions imposed by the hypothesis. Since the distributions of test statistics for censored data are often unknown and very complicated due to the unknown distributions of the censoring variables, it is of great interest to investigate possible remedies of the usual bootstrap in order to provide the critical values for the tests. Examples show that in certain situations, there are no obvious general remedies except the m out of n bootstrap. This research is primarily motivated by statistical inference problems using incomplete data which are frequently encountered in medical and reliability studies. In particular, doubly censored data and interval censored data occur in breast cancer research and AIDS research, respectively. The usual estimation and testing procedures for complete data are not directly applicable to such complicated incomplete data, and statistical analysis is lacking. The objective of this research is to investigate some general methods which will directly facilitate research in other fields, such as medicine.

9510376 任 摘要 本研究涉及使用各种类型的删失数据的统计推断问题，包括右删失、双重删失、区间删失、左截断-右删失和双变量删失数据。估计、测试和不完整数据的置信区间都在考虑之中。该研究的一个目标是研究一种新的重采样方法，称为杠杆引导法，从而避免在某些情况或某些复杂模型下将完整数据的通常估计和测试程序扩展到不完整数据的困难。到目前为止，针对不完整数据开发的程序是临时构建的。杠杆引导程序不依赖于这些临时扩展。该研究将重点研究杠杆引导在一些不完整数据的重要统计推断问题中的一致性，例如经验似然推断、非参数似然置信带、线性回归模型、两个随机变量的独立性检验、检验在一些半参数变点模型、混合模型和有偏抽样问题中。该研究的另一个目标是调查使用各种审查数据的假设检验问题中 m out of n bootstrap 的一致性，即对少于 n 个观察值进行重采样。众所周知，当人们试图在半参数（受限非参数）假设下估计检验统计量的分布并忽略假设施加的限制时，通常的非参数引导程序（n 中的 n 引导程序）会失败。由于审查数据的检验统计量的分布通常是未知的，并且由于审查变量的未知分布而非常复杂，因此研究通常的引导程序的可能补救措施以便为检验提供临界值是非常有意义的。示例表明，在某些情况下，除了 m out of n bootstrap 之外，没有明显的通用补救措施。 这项研究的主要动机是使用医学和可靠性研究中经常遇到的不完整数据的统计推断问题。特别是，双重审查数据和间隔审查数据分别出现在乳腺癌研究和艾滋病研究中。通常的完整数据估计和检验程序不能直接适用于这种复杂的不完整数据，缺乏统计分析。本研究的目的是研究一些通用方法，这些方法将直接促进其他领域（例如医学）的研究。