Computationally Efficient Nonparametric Importance Sampling

Details Computationally Efficient Nonparametric Importance Sampling Computationally Efficient Nonparametric Importance Sampling

2008-05-23

arxiv.org/abs/0805.3591v2

Journal of the American Statistical Association, 2009, 104, 788-802

Statistics

Methodology

29 pages, 7 figures

Scientific paper

The variance reduction established by importance sampling strongly depends on the choice of the importance sampling distribution. A good choice is often hard to achieve especially for high-dimensional integration problems. Nonparametric estimation of the optimal importance sampling distribution (known as nonparametric importance sampling) is a reasonable alternative to parametric approaches.In this article nonparametric variants of both the self-normalized and the unnormalized importance sampling estimator are proposed and investigated. A common critique on nonparametric importance sampling is the increased computational burden compared to parametric methods. We solve this problem to a large degree by utilizing the linear blend frequency polygon estimator instead of a kernel estimator. Mean square error convergence properties are investigated leading to recommendations for the efficient application of nonparametric importance sampling. Particularly, we show that nonparametric importance sampling asymptotically attains optimal importance sampling variance. The efficiency of nonparametric importance sampling algorithms heavily relies on the computational efficiency of the employed nonparametric estimator. The linear blend frequency polygon outperforms kernel estimators in terms of certain criteria such as efficient sampling and evaluation. Furthermore, it is compatible with the inversion method for sample generation. This allows to combine our algorithms with other variance reduction techniques such as stratified sampling. Empirical evidence for the usefulness of the suggested algorithms is obtained by means of three benchmark integration problems. As an application we estimate the distribution of the queue length of a spam filter queueing system based on real data.

Affiliated with

Also associated with

No associations

Rating

Computationally Efficient Nonparametric Importance Sampling does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Computationally Efficient Nonparametric Importance Sampling, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computationally Efficient Nonparametric Importance Sampling will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-500270