The Annals of Statistics

Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments

Valentine Genon-Catalot and Catherine Larédo

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Abstract

We prove a global asymptotic equivalence of experiments in the sense of Le Cam’s theory. The experiments are a continuously observed diffusion with nonparametric drift and its Euler scheme. We focus on diffusions with nonconstant-known diffusion coefficient. The asymptotic equivalence is proved by constructing explicit equivalence mappings based on random time changes. The equivalence of the discretized observation of the diffusion and the corresponding Euler scheme experiment is then derived. The impact of these equivalence results is that it justifies the use of the Euler scheme instead of the discretized diffusion process for inference purposes.

Article information

Source
Ann. Statist. Volume 42, Number 3 (2014), 1145-1165.

Dates
First available in Project Euclid: 20 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.aos/1403276910

Digital Object Identifier
doi:10.1214/14-AOS1216

Mathematical Reviews number (MathSciNet)
MR3224284

Zentralblatt MATH identifier
1246.62137

Subjects
Primary: 62B15: Theory of statistical experiments 62G20: Asymptotic properties
Secondary: 62M99: None of the above, but in this section 60J60: Diffusion processes [See also 58J65]

Keywords
Diffusion process discrete observations Euler scheme nonparametric experiments deficiency distance Le Cam equivalence

Citation

Genon-Catalot, Valentine; Larédo, Catherine. Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments. Ann. Statist. 42 (2014), no. 3, 1145--1165. doi:10.1214/14-AOS1216. https://projecteuclid.org/euclid.aos/1403276910


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