this paper explores a technique for variable and model selection using R-splines. R-splines are a recently proposed extension to thin plate splines with a modification to the roughness penalty that allows for a reduced polynomial component to be fit. The key model selection idea is a two-stage approach. First, the important explanatory variables are identified using a specific type of R-spline. Then these variables are used to fit different R-spline models from which the most desirable is chosen. This new method is then compared to all subset regressions by leaps and bounds and regression trees. An application of the methodology is also discussed. KEY WORDS: Thin plate spline, nonparametric, response surface, roughness penalty, leaps and bounds all subset regressions, regression trees. 1. INTRODUCTION This paper focuses on a nonparametric method for fitting response surfaces known as R-splines (Hardy and Nychka, 2000) which are a recently proposed extension to thin plate splines (Wahba, 1990, Silverman c fl 1999? American Statistical Association and the American Society for Quality Control TECHNOMETRICS, Month? 1999, VOL. , NO. D R A F T July 12, 2000, 6:40pm D R A F T 2 !Author Name(s)? and Green, 1994). This research was motivated by a specific application with twelve potential independent variables. If the functional form(s) of the variables must be designated, for example, x,
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