Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise

Shogo H. Nakakita (), Yusuke Kaino and Masayuki Uchida
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Shogo H. Nakakita: Osaka University
Yusuke Kaino: Osaka University
Masayuki Uchida: Osaka University

Annals of the Institute of Statistical Mathematics, 2021, vol. 73, issue 1, No 9, 177-225

Abstract: Abstract We consider adaptive maximum-likelihood-type estimators and adaptive Bayes-type ones for discretely observed ergodic diffusion processes with observation noise whose variance is constant. The quasi-likelihood functions for the diffusion and drift parameters are introduced and the polynomial-type large deviation inequalities for those quasi-likelihoods are shown to see the asymptotic properties of the adaptive Bayes-type estimators and the convergence of moments for both adaptive maximum-likelihood-type estimators and adaptive Bayes-type ones.

Keywords: Bayes-type estimation; Convergence of moments; Diffusion processes; Observation noise; Quasi-likelihood analysis; Stochastic differential equations (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10463-020-00746-3

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