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.

样条平滑方法在简单的实现和快速计算方面具有很大的优势。该方法成为半参数和非参数回归建模领域中最突出的技术之一。该提案的主要目的是研究两种基于样条的方法的推论方面。一个是对广义回归中分类响应数据的准样性估计，另一个是经验可能性估计，它带来了类似于参数可能性的效率属性，并保留非参数程序的无分布特征。具体而言，PI向i）提出了i）为广义样条回归模型制定强大的估计和测试程序； ii）在广义添加剂模型中使用线性混合模型和惩罚性花键之间的等效性； iii）将自由结的样条扩展到广义回归，以改善多项式样条估计器的经验行为； iv）通过考虑与样本大小的约束数量来研究部分线性模型中线性系数的样条置信区域。预计，从广泛的应用和社会科学领域（包括生物化学，生物化学，生物统计学，生物统计学，流行病学和经济学）中，研究人员对研究人员的广泛感兴趣。例如，研究结果适用于乙醇与二元结果的癌症风险之间的剂量反应关系的癌症研究，以及对海床上物种数量与空间坐标之间的关系的动物群研究，其中误差分布未完全指定。提出的程序是曲线估计的新的高度可用工具，并在通用回归模型相关的数据分析中模型诊断。出于教育目的，PI计划开发与拟议主题有关的新的高级主题课程，以指导本科生或研究生，因此使他们参与了拟议的研究和相关项目。