Penalized likelihood method can be used for hazard estimation with lifetime data that are right-censored, left-truncated, and possibly with covariates. This thesis consists of three parts. The first two parts address issues in the penalized likelihood method for single event lifetime data, and...

This thesis consists of two parts. In chapter 2, we focus on optimal smoothing with correlated data and chapter 3 is devoted to marginal semiparametric modelling of longitudinal/clustered data. Penalized likelihood method offers versatile smoothing techniques in a variety of stochastic settings,...

Generalized cross-validation (GCV) is a popular method for choosing the smoothing parameter in generalized spline smoothing when there are independent errors with common unknown variance. When data points are replicated, one can choose the smoothing parameter by minimizing one of three...

Penalized likelihood method is among the most effective tools for nonparametric multivariate function estimation. Recently, a generic computation-oriented asymptotic theory has been developed in the density estimation setting, and been extended to other settings such as conditional density...

Smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with Gaussian responses. The computation of smoothing splines is generally of the order "O"("n"-super-3), "n" being the sample size, which severely limits its practical...

This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with nonhomogeneous smoothness across the domain. Two challenging issues arising in this context are the evaluation of the equivalent kernel and the determination of a local...

This paper concerns semiparametric regression models with additive nonparametric components and high dimensional parametric components under sparsity assumptions. To achieve simultaneous model selection for both nonparametric and parametric parts, we introduce a penalty that combines the...

Nonparametric smoothing under shape constraints has recently received much well-deserved attention. Powerful methods have been proposed for imposing a single shape constraint such as monotonicity and concavity on univariate functions. In this paper, we extend the monotone kernel regression...