Electronic Journal of Statistics

Importance sampling and its optimality for stochastic simulation models

Yen-Chi Chen and Youngjun Choe

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 13, Number 2 (2019), 3386-3423.

Dates
Received: October 2018
First available in Project Euclid: 25 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1569377057

Digital Object Identifier
doi:10.1214/19-EJS1604

Mathematical Reviews number (MathSciNet)
MR4010983

Zentralblatt MATH identifier
07113721

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62G86: Nonparametric inference and fuzziness 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]

Keywords
Nonparametric estimation stochastic simulation model oracle property variance reduction Monte Carlo

Rights
Creative Commons Attribution 4.0 International License.

Citation

Chen, Yen-Chi; Choe, Youngjun. Importance sampling and its optimality for stochastic simulation models. Electron. J. Statist. 13 (2019), no. 2, 3386--3423. doi:10.1214/19-EJS1604. https://projecteuclid.org/euclid.ejs/1569377057


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