Estimation of Regression Model Using a Two Stage Nonparametric Approach

Copyright © 2013 Desale Habtzghi, Jin-Hong Park. This is an open access article distributed under the Creative Commons Attribu-tion License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Based on the empirical or theoretical qualitative information about the relationship between response variable and co-variates, we propose a new approach to model polynomial regression using a shape restricted regression after estimating the direction by sufficient dimension reduction. The purpose of this paper is to illustrate that in the absence of prior in-formation other than the shape constraints, our approach provides a flexible fit to the data and improves regression pre-dictions. We use central subspace to estimate the directions and fit a final model by shape restricted regression, when the shape is known or is stipulated from empirical inspection. Comparisons with an alternative nonparametric regres-sion are included. Simulated and real data analyses are conducted to illustrate the performance of our approach