A FAST Method for Nested Estimation

Guo Liang (), Kun Zhang () and Jun Luo ()
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Guo Liang: Institute of Statistics and Big Data, Renmin University of China, Beijing 100872, China
Kun Zhang: Institute of Statistics and Big Data, Renmin University of China, Beijing 100872, China
Jun Luo: Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200240, China

INFORMS Journal on Computing, 2024, vol. 36, issue 6, 1481-1500

Abstract: Nested estimation involves estimating an expectation of a function of a conditional expectation and has many important applications in operations research and machine learning. Nested simulation is a classic approach to this estimation, and the convergence rate of the mean squared error (MSE) of nested simulation estimators is only of order Γ − 2 / 3 , where Γ is the simulation budget. To accelerate the convergence, in this paper, we establish a jackkniFe-bAsed neSted simulaTion (FAST) method for nested estimation, and a unified theoretical analysis for general functions in the nested estimation shows that the MSE of the proposed method converges at the faster rate of Γ − 4 / 5 or even Γ − 6 / 7 . We also provide an efficient algorithm that ensures the estimator’s MSE decays at its optimal rate in practice. In numerical experiments, we apply the proposed estimator in portfolio risk measurement and Bayesian experimental design in operations research and machine learning areas, respectively, and numerical results are consistent with the theory presented.

Keywords: nested estimation; nested simulation; convergence rate; jackknife; bootstrap (search for similar items in EconPapers)
Date: 2024
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