We illustrate through examples that those nonparametric Bayes estimates based on the Bernstein-Dirichlet process are more robust to sample variation and tend to have smaller estimation errors than those based on the Dirichlet process. In certain settings, the new estimators can even outperform Stein's estimator and Efron and Morris's limited translation estimator. Chapter 3 examines the asymptotic behavior of the correlation pursuit stepwise variable selection procedure that has been proposed recently by (Zhong et al ., 2008). More specifically, we analyze the asymptotic distribution of the test statistics under the null hypothesis of no effect for selected predictors and the power of the test under the alternative hypothesis. We also compare the new procedure with the classical linear regression algorithm for linear models, and discuss the possibility of generalizing the method to multiple index models.