Importance Sampling and its Optimality for Stochastic Simulation Models

TL;DR

This paper develops a theoretical framework for importance sampling in stochastic simulation models, proposing a two-stage procedure with regression to optimize variance reduction and demonstrating its effectiveness through numerical examples.

Contribution

It introduces a novel two-stage importance sampling method with regression, analyzing its variance reduction and oracle properties for stochastic simulation estimation.

Findings

Variance reduction rates are improved with the proposed method.

Both parametric and nonparametric regressions show oracle properties.

Empirical evaluations demonstrate significant performance gains.

Abstract

We consider the problem of estimating an expected outcome from a stochastic simulation model. Our goal is to develop a theoretical framework on importance sampling for such estimation. By investigating the variance of an importance sampling estimator, we propose a two-stage procedure that involves a regression stage and a sampling stage to construct the final estimator. We introduce a parametric and a nonparametric regression estimator in the first stage and study how the allocation between the two stages affects the performance of the final estimator. We analyze the variance reduction rates and derive oracle properties of both methods. We evaluate the empirical performances of the methods using two numerical examples and a case study on wind turbine reliability evaluation.