Empirical likelihood with infinitely many constraints

具有无限多个约束的经验似然

• 批准号: 0906551
• 负责人: Anton Schick
• 金额: $ 13万
• 依托单位: SUNY at Binghamton
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0906551&HistoricalAwards=false
• 关键词: Empirical; likelihood; infinitely; many; constraints

A powerful method to do inference in models with finitely many parametric constraints is the empirical likelihood approach.This nonparametric maximization method was originally introduced by Owen in order to construct confidence regions for the underlying parameter.In the mean time the empirical likelihood method has been shown to also result in efficient estimation and testing. Needed are generalizations of this method that allow for semiparametric constraints and allow for infinitely many (parametric or semiparametric) constraints.The investigator extends the scope of the empirical likelihood into these two directions. This research advances the theory of estimation in semiparametric models and provides new methods to efficiently analyze data in a wide array of concrete problems. In the process technical problems of independent interest such a central limit theorems for quadratic forms with increasing dimensions are solved.Semiparametric models are widespread in many fields that use statistics.Although this research is theoretical in nature, it has a strong practical impact by providing more effective inference methods for all those fields.For example, results on time series have applications in economic forecasting and in mathematical finance; results on bivariate models have applications in actuarial sciences and in medical research. In medical research bivariate data naturally arise as pre- and post-treatment measurements.The research will provide ample opportunities to prepare graduate students for careers in both industry and academics.

在具有有限多个参数约束的模型中进行推断的一种强有力的方法是经验似然方法。这种非参数极大化方法最初是由Owen提出的，目的是为基础参数构造置信域。同时，经验似然方法也被证明是有效的估计和检验方法。需要的是这种方法的推广，它允许半参数约束和无限多(参数或半参数)约束。研究者将经验似然的范围扩展到这两个方向。这一研究推进了半参数模型的估计理论，并为在广泛的具体问题中有效地分析数据提供了新的方法。在这一过程中，解决了增维二次型的中心极限定理等独立感兴趣的技术问题。半参数模型广泛存在于许多使用统计学的领域。虽然这项研究具有理论性质，但它通过为所有这些领域提供更有效的推理方法，具有很强的实际影响。例如，关于时间序列的结果在经济预测和数学金融中有应用；关于二元模型的结果在精算科学和医学研究中有应用。在医学研究中，双变量数据自然会作为治疗前和治疗后的衡量标准出现。这项研究将为研究生在行业和学术界的职业生涯提供充足的机会。