Local polynomial regression is a useful non-parametric regression tool to explore fine data structures and has been widely used in practice. We propose a new non-parametric regression technique called "local composite quantile regression smoothing" to improve local polynomial regression further....

Ultra-high dimensional data often display heterogeneity due to either heteroscedastic variance or other forms of non-location-scale covariate effects. To accommodate heterogeneity, we advocate a more general interpretation of sparsity, which assumes that only a small number of covariates...

In this dissertation, several new statistical procedures in nonparametric and semiparametric models are proposed. The concerns of the research are efficiency, robustness and sparsity.In Chapter 3, we propose complete composite quantile regression (CQR) procedures for estimating both the...

Here, we describe a unique probabilistic evaluation of the 20, naturally occurring, amino acids and their distributions within the Swiss-Prot and Complete Human Genebank databases. We have developed a computational technique that imparts both directionality and length constraints into searches...