THE SEQUENTIAL BOOTSTRAP: A COMPARISON WITH REGULAR BOOTSTRAP

Abstract

Based on Bradley Efron's observation that individual resamples in the regular bootstrap have support on approximately 63% of the original observations, C. R. Rao, P. K. Pathak and V. I. Koltchinskii [1]have proposed a sequential resampling scheme. This sequential bootstrap stabilizes the information content of each resample by fixing the number of unique observations and letting N, the number of observatons in each resample, vary. The Rao-Pathak-Koltchinskii paper establishes the asymptotic correctness (consistency) of the sequential bootstrap. The main object of our investigation is to study the empirical properties of the Rao-Pathak-Koltchinskii sequential bootstrap as compared to the regular bootstrap. In all our settings, sequential bootstrap performs as well or better than regular bootstrap. In the particular case where we estimate standard errors of sample medians, we find that sequential bootstrap outperforms regular bootstrap by reducing variability in the final bootstrap estimates.

Keywords:

• Bootstrap resampling
• Quantile estimation
• Sample median

ACKNOWLEDGMENT

We wish to express our sincere thanks to the reviewer for his helpful and constructive comments.