Further Studies on Weighted Empirical Likelihood

加权经验似然的进一步研究

• 批准号: 0604488
• 负责人: Jian-Jian Ren
• 金额: $ 13.86万
• 依托单位: The University of Central Florida Board of Trustees
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604488&HistoricalAwards=false
• 关键词: Further; Studies; Weighted; Empirical; Likelihood

ABSTRACT:Since Owen (1988), the empirical likelihood method has been developed to construct tests and confidence sets based on nonparametric likelihood ratio. Studies have shown that the empirical likelihood ratio inferences are of comparable accuracy to alternative methods. However, so far the applications of empirical likelihood method to censored data are relatively few and are mainly focused on the right censored data. In this context, the PI discovered in her 2001-paper that a new likelihood function, called weighted empirical likelihoodfunction, has the potential to facilitate the research on a broad class of nonparametric and semiparametric statistics for various types of incomplete data, including doubly censored data, interval censored data, and partly interval-censored data. It is shown that weighted empirical likelihood may be viewed as the asymptotic version of Owen's empirical likelihood function for censored data. In the past few years, the PI's investigationshows that the weighted empirical likelihood indeed provides a useful tool to deal with statistical inference problems with complicated types of censored data which are otherwise quite difficult to handle. The objective of this current project is to further study the applications of weighted empirical likelihood in providing solutions for several important nonparametric or semiparametric statistical inference problems in survivalanalysis with various types of censored data. The issues under consideration include: (1) extension of the weighted empirical likelihood to deal with p-dimensional variables; (2) further applications of the weighted empirical likelihood to estimation or model assessment problems associated with estimating equations, profile likelihood and some important survival models; (3) coverage accuracy of weighted empirical likelihood ratio confidence intervals; (4) comparison with alternative methods.Incomplete data are frequently encountered in medical follow-up and reliability studies. Recently, statisticians are paying more attention to some more complicated types of incomplete data, such as doublycensored data, interval censored data, partly interval-censored data, truncated data, etc., as these data occur in important clinical trials and scientific research. For instance, doubly censored data were encountered in a recent study of primary breast cancer, interval censored data were encountered in AIDS research, partly interval-censored data were encountered in heart disease and diabetes studies,and doubly truncated data were encountered in astronomical research. Up to now, the statistical research on these more complicated types of incomplete data still generally lags behind that on right censored data,mainly because it is technically much more challenging. The expected results of this project are better understandingof the technique of weighted empirical likelihood, and providing solutions for several important statistical inference problems associated with some widely used survival models in biomedical research and epidemiological studies when observed data are right censored, doubly censored, interval censored, or partlyinterval-censored.

摘要：自Owen（1988）以来，经验似然方法被发展为基于非参数似然比来构造检验和置信集。研究表明，经验似然比推断的准确性与其他方法相当。然而，到目前为止，经验似然方法在删失数据中的应用相对较少，且主要集中在右删失数据上。在这种情况下，PI在她2001年的论文中发现，一种新的似然函数，称为加权经验似然函数，有可能促进各种类型的不完全数据的非参数和半参数统计的研究，包括双删失数据，区间删失数据和部分区间删失数据。它表明，加权经验似然可被视为欧文的经验似然函数的渐近版本的删失数据。在过去的几年里，PI的调查表明，加权经验似然确实提供了一个有用的工具来处理统计推断问题的复杂类型的删失数据，否则是相当困难的处理。本课题的目的是进一步研究加权经验似然法在解决不同类型删失数据生存分析中几个重要的非参数或半参数统计推断问题中的应用。研究的问题包括：（1）将加权经验似然法推广到p维变量，（2）进一步应用加权经验似然法处理与估计方程、剖面似然和一些重要生存模型相关的估计或模型评估问题，（3）加权经验似然比置信区间的覆盖精度，（4）加权经验似然比置信区间的覆盖精度，（5）加权经验似然比置信区间的覆盖精度，（6）加权经验似然比置信区间的覆盖精度，（7）加权经验似然比置信区间的覆盖精度，（8）加权经验似然比置信区间的覆盖精度，（9）加权经验似然比置信区间的覆盖精度，（10）加权经验似然比置信区间的覆盖精度。（4）与其他方法的比较在医学随访和可靠性研究中经常遇到不完整数据。近年来，一些更复杂的不完全数据类型，如双删失数据、区间删失数据、部分区间删失数据、截断数据等，越来越受到统计学家的关注，因为这些数据出现在重要的临床试验和科学研究中。例如，在最近的一项原发性乳腺癌研究中遇到了双重删失数据，在艾滋病研究中遇到了区间删失数据，在心脏病和糖尿病研究中遇到了部分区间删失数据，在天文学研究中遇到了双重截断数据。到目前为止，对这些更复杂类型的不完全数据的统计研究仍然普遍落后于右删失数据，主要是因为它在技术上更具挑战性。本项目的预期结果是更好地理解加权经验似然技术，并解决了一些重要的统计推断问题，这些问题与生物医学研究和流行病学研究中广泛使用的生存模型相关，当观察数据是右删失，双删失，区间删失或部分区间删失时。