×

Antithetic variates for Monte Carlo estimation of probabilities. (English) Zbl 0552.65097

The paper explores the possibilities of using the variance reduction technique of antithetic variates for the estimation of probabilities, in particular rejection probabilities of statistical tests. The minimal variance via the use of k-tuples of antithetic variates is derived, some results are given.
Reviewer: G.Jumarie

MSC:

65C99 Probabilistic methods, stochastic differential equations
65C05 Monte Carlo methods
62J10 Analysis of variance and covariance (ANOVA)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Andrews D. E., Princeton University Press (1972)
[2] Brent R. P., Comm. Ass. Comp. Mach. 17 pp 704– (1974)
[3] DOI: 10.1080/02331938108842712 · Zbl 0467.60004
[4] J. M. Hammersley, and D. C. Handscomb(1964 ). Monte Carlo methods ,Methuen, London. · Zbl 0121.35503
[5] Hammersley J. M., Proc. Combr. Phil Soc. 52 pp 449– (1956)
[6] Kennedy W. J., Statistical computing (1981)
[7] DOI: 10.1007/BF00536046 · Zbl 0377.60022
[8] Lehmann E. L., Nonparametrics (1975) · Zbl 0354.62038
[9] DOI: 10.2307/2346729 · Zbl 0438.62037
[10] DOI: 10.1007/BF02056901 · Zbl 0535.62008
[11] DOI: 10.2307/2347234
[12] Snijders T. A. B., Statistica Neerlandica 37 pp 150– (1983)
[13] Tukey J. W., Proc. Comb. Phil. Soc. 53 pp 923– (1957)
[14] DOI: 10.1214/aos/1176343660 · Zbl 0367.62022
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.