Spline-based Empirical Likelihood and Qausi-likelihood Estimation

样条光顺方法具有实现简单、计算速度快等优点。该方法成为半参数和非参数回归建模领域最突出的技术之一。这项建议的主要目的是调查两个样条为基础的方法的推理方面。一种是广义回归中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，并保留了非参数过程的分布自由性质。具体而言，PI建议i）为广义样条回归模型开发稳健估计和检验程序; ii）在广义可加模型中使用线性混合模型和惩罚样条之间的等价性进行线性检验; iii）将自由结点样条扩展到广义回归，以改善多项式样条估计的经验行为;（iv）通过经验似然法研究部分线性模型中线性系数的样条置信域，并考虑到约束条件的数量随样本容量的增加而增加。社会科学领域，包括生物化学，生物统计学，流行病学和经济学。例如，研究结果适用于乙醇与癌症风险之间剂量-反应关系的癌症研究，其结果为二元，以及海底物种数量与空间坐标之间关系的动物群研究，其中误差分布未完全确定。所提出的程序作为新的高度可用的工具，曲线估计和模型诊断一般回归模型相关的数据分析。为教育目的，PI计划开发一个与拟议主题相关的新高级主题课程，以指导本科生或研究生，从而使他们参与拟议的研究和相关项目。

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.