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，已经开发了基于非参数可能性比率的经验可能性方法来构建测试和置信度。研究表明，经验可能性比推断与替代方法具有可比的精度。但是，到目前为止，经验可能性方法在审查数据中的应用相对较少，并且主要集中在正确的审查数据上。 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.结果表明，加权经验可能性可能被视为欧文对审查数据的经验可能性函数的渐近版本。在过去的几年中，PI的调查表明，加权经验可能性确实为处理复杂类型的审查数据类型的统计推断问题提供了有用的工具，否则很难处理。该当前项目的目的是进一步研究加权经验可能性在为几种重要的非参数或半参数统计推论提供生存分析中的解决方案，并使用各种各样的审查数据。所考虑的问题包括：（1）加权经验可能性的扩展，以处理P维变量； （2）加权经验可能性进一步应用于与估计方程，概况可能性和一些重要生存模型相关的估计或模型评估问题； （3）加权经验可能性比置信区间的覆盖精度； （4）与替代方法的比较。在医学随访和可靠性研究中经常遇到完整数据。最近，统计学家正在更加关注一些更复杂类型的不完整数据，例如双重审查的数据，间隔审查的数据，部分间隔经过的数据，截断数据等，因为这些数据发生在重要的临床试验和科学研究中。例如，在最新的原发性乳腺癌研究中遇到了双重审查的数据，在艾滋病研究中遇到了间隔的审查数据，在心脏病和糖尿病研究中遇到了部分间隔进行的数据，并在天文学研究中遇到了双重截断的数据。到目前为止，对这些更复杂类型的不完整数据的统计研究通常仍然落后于右审查数据，这主要是因为它在技术上更具挑战性。该项目的预期结果是更好地了解加权经验可能性的技术，并为生物医学研究和流行病学研究中一些广泛使用的生存模型相关的几个重要统计推断问题提供解决方案，当时观察到的数据经过正确的审查，双重审查，双重审查，间隔审查，或部分审查或部分审查。