Quasi-likelihood analysis of an ergodic diffusion plus noise

2018/06/25 by Nakakita, Shogo H., Uchida, Masayuki
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1806.09401

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 convergence of moments for those estimators.

Related

• Inference for ergodic diffusions plus noise
• Adaptive estimation and noise detection for an ergodic diffusion with observation noises
• Quasi-likelihood analysis for adaptive estimation of a degenerate diffusion process
• Data driven time scale in Gaussian quasi-likelihood inference
• Adaptive test for ergodic diffusions plus noise