Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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An importance sampling for a function of a multivariate random variable

  • Jae-Yeol Park (Department of Statistics, University of Seoul) ;
  • Hee-Geon Kang (Department of Statistics, University of Seoul) ;
  • Sunggon Kim (Department of Statistics, University of Seoul)
  • Received : 2023.09.11
  • Accepted : 2023.10.24
  • Published : 2024.01.31
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Abstract

The tail probability of a function of a multivariate random variable is not easy to estimate by the crude Monte Carlo simulation. When the occurrence of the function value over a threshold is rare, the accurate estimation of the corresponding probability requires a huge number of samples. When the explicit form of the cumulative distribution function of each component of the variable is known, the inverse transform likelihood ratio method is directly applicable scheme to estimate the tail probability efficiently. The method is a type of the importance sampling and its efficiency depends on the selection of the importance sampling distribution. When the cumulative distribution of the multivariate random variable is represented by a copula and its marginal distributions, we develop an iterative algorithm to find the optimal importance sampling distribution, and show the convergence of the algorithm. The performance of the proposed scheme is compared with the crude Monte Carlo simulation numerically.

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Acknowledgement

The authors would like to thank the anonymous reviewers for their comments and suggestions on the first draft of this paper. Their suggestions have greatly improve the quality of the paper. This work was supported by the 2021 sabbatical year research grant of the University of Seoul.

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