Weighted Empirical Likelihood

加权经验似然

• 批准号: 0204182
• 负责人: Jian-Jian Ren
• 金额: $ 10.13万
• 依托单位: The University of Central Florida Board of Trustees
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-01 至 2006-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0204182&HistoricalAwards=false
• 关键词: Weighted; Empirical; Likelihood

Proposal ID: DMS-0204182PI: Jian-Jian RenTitle: Weighted empirical likelihoodAbstract The objective of this research is to investigate the applications of a new likelihood function, called weighted empirical likelihood, in constructing confidence sets and tests for various important nonparametric or semiparametric statistical inference problems in survival analysis using different types of incomplete data, including right censored data, doubly censored data and interval censored data. Weighted empirical likelihood function is formulated in a unified form through the probability mass of the nonparametric maximum likelihood estimator for different types of incomplete data. The PI has shown that the high-order expansion of the log-likelihood ratio for a quite general class of statistics can be obtained in a unified way for various types of censored data aforementioned. Thus, with the help of the adjusted n out of n bootstrap, the weighted empirical likelihood ratio can be used to construct efficient confidence intervals or tests. The proposed procedure does not require the precise knowledge of the convergence rate of the statistic of interest, which is particularly appealing for interval censored data. All preliminary studies show that the desirable properties of weighted empirical likelihood method include accuracy, efficiency, generality, and independency of the precise knowledge of the convergence rate of the statistic of interest. In this research, the issues under consideration include: (a) Applications of weighted empirical likelihood in statistical inference problems with various types of incomplete data, including the construction of confidence intervals and tests associated with profile likelihood problems, accelerated life model, proportional hazards model, and logistic regression model, etc.; (b) Coverage accuracy of weighted empirical likelihood ratio confidence intervals; (c) Efficiency of weighted empirical likelihood inferences; (d) Comparison with alternative methods if they exist. 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 doubly censored data, 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, 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. 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 mostly on right censored data. Examples show that for complicated types of incomplete data, such as interval censored data, the investigation of the limiting distribution of log-likelihood ratio can be quite difficult. In this context, aiming to provide solutions for various difficult problems that arise in medical and scientific research, this project intends to develop reliable statistical methods based on a new likelihood function, called weighted empirical likelihood function.

提案ID：DMS-0204182PI：Jian-jian Rentitle：加权经验可能性解放这项研究的目标是调查新的可能性功能的应用，称为加权经验可能性，在构建各种重要的非参数或半统计数据的置信度中的置信集和测试中，构建置信度和测试，包括使用统计数据的数据，这些数据涉及均匀分析的数据，这些数据涉及既有统计数据均可在附近的数据双重审查数据和间隔审查数据。加权经验可能性函数以统一形式通过非参数最大似然估计量的概率质量以不同类型的不完整数据制定。 PI表明，对于上述各种审查的数据，可以以统一的方式获得相当一般的统计类别的对数可能性比率的高阶扩展。因此，借助N hootstrap的调整后的N，加权经验可能比率可用于构建有效的置信区间或测试。所提出的程序不需要精确了解感兴趣统计量的收敛速率，这特别吸引了间隔审查的数据。所有初步研究都表明，加权经验可能性方法的理想特性包括准确性，效率，一般性和对利益统计统计统计收敛率的确切知识的独立性。在这项研究中，所考虑的问题包括：（a）加权经验可能性在具有各种类型的不完整数据的统计推断问题中的应用，包括构建置信区间和与个人资料可能性问题，加速生活模型，比例危害危害模型和逻辑回归模型等相关的测试。 （b）加权经验可能性比置信区间的覆盖精度； （c）加权经验可能性推断的效率； （d）与替代方法（如果存在）进行比较。 在医学随访和可靠性研究中经常遇到不完整的数据。最近，由于这些数据发生在重要的临床试验和科学研究中，统计学家正在更加关注一些更复杂类型的不完整数据，例如双重审查数据，间隔审查数据，截断数据等。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，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。 自欧文（Owen，1988）以来，就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，并且大多在正确的审查数据上。示例表明，对于复杂类型的不完整数据（例如间隔审查数据），对数字可能性比率的限制分布的研究可能非常困难。在这种情况下，旨在为医学和科学研究中出现的各种困难问题提供解决方案，该项目旨在根据新的可能性功能（称为加权经验可能性功能功能）开发可靠的统计方法。