Resampling with Perturbing the Original Data: A New Variant of the Smoothed Bootstrap

• Activity Number: 661
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Haiyan Bai*+ and Wei Pan
• Companies: University of Central Florida and University of Cincinnati
• Keywords: resampling ; bootstrap ; smoothed bootstrap ; Monte Carlo ; simulation

Abstract

Resampling has been regarded as one of the most effective strategies for contending with small-sample problems in statistical inference; however, limitations such as dependent observations still exist with current resampling techniques including both the naïve and smoothed bootstraps. The present study introduces a new variant of the smoothed bootstrap, called the "perturbing bootstrap." The procedure of the perturbing bootstrap is methodologically different from that of the smoothed bootstrap in that, instead of sampling from the smoothed distribution, the perturbing bootstrap samples directly from the neighborhoods of the original data points with optimal perturbation. The perturbing bootstrap is not only computationally simpler than the smoothed bootstrap, but also has comparably better statistical properties than those of both the naïve and smoothed bootstraps. A Monte Carlo simulation study is conducted to compare the statistical performance of the perturbing bootstrap to those of both the naïve and smoothed bootstraps in terms of the accuracy and stability of parameter estimation. Finally, an illustrative example for implementing the perturbing bootstrap is also presented.