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2020 Parametric inference for diffusions observed at stopping times
Emmanuel Gobet, Uladzislau Stazhynski
Electron. J. Statist. 14(1): 2098-2122 (2020). DOI: 10.1214/20-EJS1708


In this paper we study the problem of parametric inference for multidimensional diffusions based on observations at random stopping times. We work in the asymptotic framework of high frequency data over a fixed horizon. Previous works on the subject (such as [10, 17, 19, 5] among others) consider only deterministic, strongly predictable or random, independent of the process, observation times, and do not cover our setting. Under mild assumptions we construct a consistent sequence of estimators, for a large class of stopping time observation grids (studied in [20, 23]). Further we carry out the asymptotic analysis of the estimation error and establish a Central Limit Theorem (CLT) with a mixed Gaussian limit. In addition, in the case of a 1-dimensional parameter, for any sequence of estimators verifying CLT conditions without bias, we prove a uniform a.s. lower bound on the asymptotic variance, and show that this bound is sharp.


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Emmanuel Gobet. Uladzislau Stazhynski. "Parametric inference for diffusions observed at stopping times." Electron. J. Statist. 14 (1) 2098 - 2122, 2020.


Received: 1 October 2018; Published: 2020
First available in Project Euclid: 13 May 2020

zbMATH: 07210996
MathSciNet: MR4097050
Digital Object Identifier: 10.1214/20-EJS1708

Primary: 60F05 , 60G40 , 60GXX , 62F12 , 62Fxx , 62Mxx

Keywords: asymptotic variance , consistent sequence of estimators , Diffusion coefficient estimation , local asymptotic mixed normality , observation at stopping times , optimal lower bound


Vol.14 • No. 1 • 2020
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