Quasi-likelihood analysis and its applications

Nakahiro Yoshida ()
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Nakahiro Yoshida: University of Tokyo

Statistical Inference for Stochastic Processes, 2022, vol. 25, issue 1, No 4, 43-60

Abstract: Abstract The Ibragimov–Khasminskii theory established a scheme that gives asymptotic properties of the likelihood estimators through the convergence of the likelihood ratio random field. This scheme is extending to various nonlinear stochastic processes, combined with a polynomial type large deviation inequality proved for a general locally asymptotically quadratic quasi-likelihood random field. We give an overview of the quasi-likelihood analysis and its applications to ergodic/non-ergodic statistics for stochastic processes.

Keywords: Ibragimov–Khasminskii theory; Quasi-likelihood; Locally asymptotically quadratic random field; Polynomial type large deviation; Quasi-maximum likelihood estimator; Quasi-Bayesian estimator; Diffusion process; Adaptive estimator; Jump-diffusion process; Lévy process; Volatility; Jump filter; Point process; Non-synchronous observations; Information criterion; Sparse estimation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11203-021-09266-0

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