Statistics and Computing

, Volume 1, Issue 1, pp 13–22 | Cite as

Quasi-random resampling for the bootstrap

  • Kim-Anh Do
  • Peter Hall
Papers

Abstract

Quasi-random sequences are known to give efficient numerical integration rules in many Bayesian statistical problems where the posterior distribution can be transformed into periodic functions on then-dimensional hypercube. From this idea we develop a quasi-random approach to the generation of resamples used for Monte Carlo approximations to bootstrap estimates of bias, variance and distribution functions. We demonstrate a major difference between quasi-random bootstrap resamples, which are generated by deterministic algorithms and have no true randomness, and the usual pseudo-random bootstrap resamples generated by the classical bootstrap approach. Various quasi-random approaches are considered and are shown via a simulation study to result in approximants that are competitive in terms of efficiency when compared with other bootstrap Monte Carlo procedures such as balanced and antithetic resampling.

Keywords

Bias bootstrap discrepancy distribution function equidistribution good lattice points Monte Carlo simulation pseudo-random quasi-random regular and irregular sequences 

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Copyright information

© Chapman and Hall Ltd 1991

Authors and Affiliations

  • Kim-Anh Do
    • 1
  • Peter Hall
    • 1
  1. 1.Statistical Sciences Division, Centre for Mathematics and ApplicationsAustralian National UniversityCanberraAustralia

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