Estimation of Regression Model Using Nonparametric Model

• Activity Number: 39
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Desale Habtzghi*+ and Jin-Hong Park
• Companies: The University of Akron and College of Charleston
• Keywords: Polynomial regression ; Sufficient dimension reduction ; Central subspace ; Nonparametric regression

Abstract

The recent literature on sufficient dimension reduction method do not place confine on the predictors that are necessary for ordinary least square, nor does it require that the dependence is restricted to meticulous conditional moments. Based on these developments for sufficient dimension reduction and qualitative information about the relationship between response variable and covariates, we propose a new approach to model a polynomial regression using a shape restricted regression. The purpose is to illustrate that, in the absence of prior information other than the shape constraints, our approach might be an acceptable alternative. In this paper, 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, scatter plot of the response variable versus the linear combination of the predictors. Comparisons with the traditional polynomial regression are included. Simulated and real data analysis are conducted to illustrate the performance of our approach.