Spline-based Empirical Likelihood and Qausi-likelihood Estimation

基于样条的经验似然和 Qausi 似然估计

• 批准号: 1107017
• 负责人: Jing Wang
• 金额: $ 8.04万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-15 至 2014-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1107017&HistoricalAwards=false
• 关键词: Spline; based; Empirical; Likelihood; Qausi

Spline smoothing method contains substantial advantages for its simple implementation and fast computation. The method becomes one of the most prominent techniques in the area of semi-parametric and nonparametric regression modeling. The main objective of this proposal is to investigate the inferential aspects of two spline-based methods. One is the quasi-likelihood estimation for categorized response data in generalized regression, and the other the empirical likelihood estimation which brings efficiency properties analogous to parametric likelihood and retains distribution-free character of nonparametric procedures. Specifically, the PI proposes to i) develop robust estimation and testing procedures for generalized spline regression models; ii) employ the equivalence between linear mixed models and penalized splines for linearity tests in generalized additive models; iii) extend free-knots spline to generalized regression in order to improve the empirical behavior of polynomial spline estimators; and iv) investigate spline confidence region of linear coefficients in partially linear models via empirical likelihood by considering the number of constraints growing with the sample sizes.The proposed projects are expected to be of broad interest to researchers from a wide range of applied and social science fields including biochemistry, biostatistics, epidemiology, and economics. For example, the research findings are applicable to a cancer research study for a dose-response relationship between ethanol and risk of cancer with binary outcomes, and a fauna study for relationship between the number of species on sea bed and the spatial coordinates where error distribution is not fully specified. The proposed procedures serve as new highly usable tools for curve estimation and model diagnosis in general regression model-related data analysis. For educational purpose, the PI plans to develop a new advanced topic course related with the proposed topics to mentor undergraduate or graduate students, and therefore involve them in proposed research and related projects.

样条光滑法具有实现简单、计算速度快等优点。该方法已成为半参数和非参数回归建模领域最突出的技术之一。本提案的主要目的是研究两种基于样条法的方法的推理方面。一种是广义回归中对分类响应数据的拟似然估计，另一种是经验似然估计，它具有类似于参数似然的有效性性质，并保持了非参数过程的无分布特性。具体地说，PI建议：i)开发广义Spline回归模型的稳健估计和检验程序；ii)在广义加性模型中使用线性混合模型和惩罚样条线性度的等价性；iii)将自由结样条扩展到广义回归，以改进多项式样条估计器的经验行为；以及iv)通过考虑约束的数量随样本量的增长，通过经验似然来研究部分线性模型中线性系数的样条置信域。例如，研究结果适用于关于酒精和癌症风险之间的剂量-反应关系的癌症研究，以及关于海底物种数量与空间坐标之间关系的动物群研究，其中误差分布没有完全明确。这些方法为一般回归模型相关数据分析中的曲线估计和模型诊断提供了新的高度可用的工具。就教育目的而言，该中心计划发展一项与建议课题有关的新的高级专题课程，以指导本科生或研究生，从而让他们参与建议的研究及相关项目。