Nonparametric Method and Hierarchical Bayesian Approach for Parameter Estimation and Prediction

Obtaining accurate estimates or prediction from available data is one of the important goals in statistical research. In this thesis, we propose two new statistical methods, with examples of application and simulation studies, to achieve this goal. The parametric penalized spline smoothing procedure is a flexible algorithm that requires no restricted parametric assumption and is proved to obtain more accurate estimates of curves and derivatives than available methods. In the second part of thesis, we propose a hierarchical Bayesian approach to estimate dynamic engineering model parameters and their mixed effects. This approach has the benefits of solving the identifiability problem of model parameters and accurately estimating these parameters from right censored data. It is further investigated with simulated data to perform predictions. Predicting quality with this method is proved to be better than that from procedures without considering censoring situation.