Jennifer Pittman, Pennsylvania State University

Adaptive Splines and Genetic Algorithms for Optimal Statistical Modeling

Due in part to the increased availability of computational power, spatially adaptive smoothing methods involving regression splines have become a rapidly developing class of nonparametric modeling techniques. Most existing algorithms for fitting adaptive splines are based on non-linear optimization and/or stepwise selection. Although computationally fast and spatially adaptive, stepwise knot selection is necessarily suboptimal while determining the best model over the space of adaptive knot splines is a very poorly behaved non-linear optimization problem. A possible alternative is to use more intensive numerical optimization techniques such as genetic algorithms to perform knot selection. A spatially adaptive modeling technique referred to as adaptive genetic splines (AGS) is introduced which combines the optimization power of a genetic algorithm with the flexibility of polynomial splines. Preliminary simulation results comparing the performance of the genetic algorithm method to other current methods, such as HAS (Luo and Wahba 1997) and SUREshrink (Donoho and Johnstone 1995), will be discussed, as well as a current application of AGS in the engineering sciences. Topics for future research will also be mentioned.