| This thesis discusses the local polynomial regression and the isotonic regression method to solve the nonparametric regression problem subject to the non-decreasing condition. To solve the continuous isotonic regression problem, Pool Adjacent Violators Algorithm (PAVA) is used by updating the local polynomial regression estimates of a large amount of quantiles of X. Considering the importance of the bandwidth selection for nonparametric fitting, a new Cross Validation (CV) method that incorporates the non-decreasing condition is proposed. Furthermore, the simulations are conducted to evaluate the performance of this CV method in comparison with the plug-in bandwidth selection method in the regression estimations. By obtaining the outcomes of L1 distance, its percentage improvement, and confidence interval bands, we conclude that the proposed CV bandwidth selection method improves the performance if sufficient data is provided. The proposed method in the weighted isotonic regression estimation outperforms others in this nonparametric regression problem because they both contribute to factor in the monotone constraint. |
