An Improved Bagging Cross-Validation Method with Second-Order Extrapolation in Bandwidth Selection

• Activity Number: 76
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Qing Wang*+ and Bruce G. Lindsay
• Companies: Williams College and Penn State
• Keywords: bagging ; bandwidth selection ; extrapolation ; kernel density estimation ; nested cross validation

Abstract

In this talk we consider a possible improvement of bagging cross validation in the context of kernel density estimation. Previous research (Marron (1987) and Hall and Robinson (2009)) has been done in reducing the variability of the conventional leave-one-out cross validated bandwidth selector using bagging plus linear extrapolation. We consider a second-order approximation for the optimal risk curve in the extrapolation stage. Extensive simulation study has shown that the bagging CV bandwidth selector with second-order extrapolation outperforms the simple linear extrapolated bagging CV method across a wide selection of distributions. To select the optimal subsample size in the bagging stage, we propose a Nested Cross Validation method which is a data-driven, automatic selection criterion. We compare the performance of the Nested Cross Validation methodology with the optimal subsample size suggested by Marron (1987). Numerical studies indicate that the second-order extrapolated bagging CV bandwidth selector with Nested Cross Validation is a promising method that achieves a smaller expected integrated squared error.