论文信息 - COUPLED SAMPLES IN SIMULATION

COUPLED SAMPLES IN SIMULATION

Assume that we wish to generate two samples of n independent identically distributed random variables, (XI, ..., X.) and (y" ..., Y.), where XI and YI have densitiesfand g, respectively. If these samples are used in a simulation, andf is close to g, it is sometimes desirable to have close simulation results. This can be achieved by insisting that both samples agree in most of their components, that is, Xi = Yi for as many i as possible under the given distributional constraints. Samples with this property are said to be optimally coupled. In this paper, we propose and study various methods of coupling two samples, a sequence of samples and an infinite family of samples.

Operations Research | Operations Research

[1] H. Scheffé. A Useful Convergence Theorem for Probability Distributions , 1947 .

[2] E. Bronshtein. Metric entropy of some classes of sets , 1997 .

[3] H. Thorisson. On Maximal and Distributional Coupling , 1986 .

[4] K. Alexander,et al. Probability Inequalities for Empirical Processes and a Law of the Iterated Logarithm , 1984 .

[5] G. Lorentz. Approximation of Functions , 1966 .

[6] Luc Devroye,et al. Sample-based non-uniform random variate generation , 1986, WSC '86.

[7] R. Serfling. A General Poisson Approximation Theorem , 1975 .

[8] L. Devroye. Non-Uniform Random Variate Generation , 1986 .

[9] J. Dehardt. Generalizations of the Glivenko-Cantelli Theorem , 1971 .

[10] L. Devroye. A Course in Density Estimation , 1987 .

[11] L. L. Cam,et al. An approximation theorem for the Poisson binomial distribution. , 1960 .

[12] L. Devroye. Bounds for the Uniform Deviation of Empirical Measures , 1982 .