Knot Selection for Least Squares and Penalized Splines

• Activity Number: 309
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Steven Spiriti*+ and Randall Eubank and Philip Smith and Dennis Young
• Companies: Arizona State University and Arizona State University and Texas Tech University and Arizona State University
• Keywords: blind random search ; genetic algorithm ; golden section ; parallel computing ; free-knot splines ; penalized splines

Abstract

We compare techniques for computing free-knot splines and penalized splines, or P-splines. Although P-splines are conventionally fitted using fixed knot locations, we examine the case where P-splines are fitted using optimal knot locations. Standard optimization algorithms do not perform adequately when optimizing the knot locations; consequently, two random search alternatives are proposed: blind search with golden section and a genetic algorithm. A simulation study is performed, comparing the free-knot algorithms to fixed-knot algorithms and to smoothing splines. It is found that the free-knot algorithms outperform their fixed-knot alternatives.