TreeMARS Models for Use in Stochastic Dynamic Programming Framework

• Activity Number: 306
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Subrat Sahu*+ and Victoria Chen and Seoung Bum Kim
• Companies: The University of Texas at Arlington and The University of Texas at Arlington and Korea University
• Keywords: Regression Splines ; Regression Trees ; Statistical Modeling ; Value Function Approximation ; Stochastic Dynamic Programming ; TreeMARS Models

Abstract

Seeking to develop a flexible, nonparametric statistical modeling method which can capture complex non-linearity in data comprised of a mix of quantitative and qualitative variables and can be used to approximate future value functions and to estimate state transition functions in stochastic dynamic programming (SDP) problems with a mix of continuous and categorical state variables, we present a tree-MARS model that first fits a regression tree model, and then uses multivariate adaptive regression splines (MARS) to refine the model at the terminal nodes of the tree. Comparisons are made to the tree-regression model which uses a similar concept, but only permits the use of linear regression at the terminal nodes.