Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient

Romain Guy, Catherine Larédo and Elisabeta Vergu

Stochastic Processes and their Applications, 2014, vol. 124, issue 1, 51-80

Abstract: We consider a multidimensional diffusion X with drift coefficient b(α,Xt) and diffusion coefficient ϵσ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔ for k=1…n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small ϵ. We obtain consistent and asymptotically normal estimators of α for fixed Δ and ϵ→0 and of (α,β) for Δ→0 and ϵ→0 without any condition linking ϵ and Δ. We compare the estimators obtained with various methods and for various magnitudes of Δ and ϵ based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework.

Keywords: Minimum contrast estimators; Low frequency data; High frequency data; Epidemic data (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:1:p:51-80

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DOI: 10.1016/j.spa.2013.07.009

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