Spline-based Empirical Likelihood and Qausi-likelihood Estimation

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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.