TY - JOUR

T1 - Statistical errors in Monte Carlo-based inference for random elements

AU - Shimizu, Yasutaka

N1 - Publisher Copyright:
Copyright © 2020, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/5/5

Y1 - 2020/5/5

N2 - Monte Carlo simulation is useful to compute or estimate expected functionals of random elements if those random samples are possible to be generated from the true distribution. However, when the distribution has some unknown parameters, the samples must be generated from an estimated distribution with the parameters replaced by some estimators, which causes a statistical error in Monte Carlo estimation. This paper considers such a statistical error and investigates the asymptotic distributions of Monte Carlo-based estimators when the random elements are not only the real valued, but also functional valued random variables. We also investigate expected functionals for semimartingales in details. The consideration indicates that the Monte Carlo estimation can get worse when a semimartingale has a jump part with unremovable unknown parameters.MSC Codes 65C05, 62G20, 62M20

AB - Monte Carlo simulation is useful to compute or estimate expected functionals of random elements if those random samples are possible to be generated from the true distribution. However, when the distribution has some unknown parameters, the samples must be generated from an estimated distribution with the parameters replaced by some estimators, which causes a statistical error in Monte Carlo estimation. This paper considers such a statistical error and investigates the asymptotic distributions of Monte Carlo-based estimators when the random elements are not only the real valued, but also functional valued random variables. We also investigate expected functionals for semimartingales in details. The consideration indicates that the Monte Carlo estimation can get worse when a semimartingale has a jump part with unremovable unknown parameters.MSC Codes 65C05, 62G20, 62M20

KW - Asymptotic distribution, diffusion processes

KW - Expected functionals

KW - Monte Carlo estimator

KW - Semimartingales

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M3 - Article

AN - SCOPUS:85094017295

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

ER -