Statistical errors in Monte Carlo-based inference for random elements

Research output: Contribution to journalArticlepeer-review

Abstract

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

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2020 May 5

Keywords

  • Asymptotic distribution, diffusion processes
  • Expected functionals
  • Monte Carlo estimator
  • Semimartingales

ASJC Scopus subject areas

  • General

Fingerprint Dive into the research topics of 'Statistical errors in Monte Carlo-based inference for random elements'. Together they form a unique fingerprint.

Cite this