Two-Stage Subsampling-Extrapolation Techniques in Bandwidth Selection

• Activity Number: 305
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Qing Wang*+ and Bruce G. Lindsay
• Companies: Williams College and The Pennsylvania State University
• Keywords: bandwidth selection ; cross-validation ; extrapolation ; subsampling ; U-statistic

Abstract

In this talk we focus on the application of cross-validation in risk estimation and bandwidth selection under the context of kernel density estimation. We construct U-statistic form estimates for the risk and propose a two-stage, subsampling-extrapolation, bandwidth selection procedure which is based on first evaluating the risk at a fictional sample size m (m< sample n) and then extrapolate the optimal bandwidth from m to n. This two-stage method can dramatically reduce the variability of the conventional unbiased cross-validation bandwidth selector. We have also noticed that the simple first-order extrapolated bandwidth selector is equivalent to the rescaled bagging CV method in Hall and Robinson (2009) if one sets the bootstrap size equal to the fictional sample size. However, our simple expression for the U risk estimator enables us to compute the aggregated risk much more efficiently than bootstrapping. Furthermore, we developed a second-order extrapolation technique as an alternative to improve the performance of approximating the true optimal bandwidth.