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 the n-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.
Original language | English (US) |
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Pages (from-to) | 13-22 |
Number of pages | 10 |
Journal | Statistics and Computing |
Volume | 1 |
Issue number | 1 |
DOIs | |
State | Published - Sep 1991 |
Externally published | Yes |
Keywords
- Bias
- Monte Carlo simulation
- bootstrap
- discrepancy
- distribution function
- equidistribution
- good lattice points
- pseudo-random
- quasi-random
- regular and irregular sequences
ASJC Scopus subject areas
- Theoretical Computer Science
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Computational Theory and Mathematics