Partial quasi-likelihood analysis

Yoshida, Nakahiro

doi:10.1007/s42081-018-0006-6

Cited by 5 publications

(3 citation statements)

References 32 publications

(49 reference statements)

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“…Nothing to say, this is a quasilikelihood approach. This problem is of practical importance because implementation is easy with the Gaussian quasi-likelihood, as YUIMA (Brouste et al 2014, Iacus andYoshida 2018).…”

Section: Gaussian Quasi-likelihood To Lévy Driven Stochastic Differen...mentioning

confidence: 99%

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Quasi-likelihood analysis and its applications

Yoshida

2022

Stat Inference Stoch Process

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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.

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Section: Gaussian Quasi-likelihood To Lévy Driven Stochastic Differen...mentioning

confidence: 99%

“…Related papers are Masuda and Shimizu (2017) and Suzuki and Yoshida (2020). Partial quasi-likelihood analysis is another direction of extension of the theory (Yoshida 2018).…”

Section: Non-synchronous Observationsmentioning

confidence: 99%

Quasi-likelihood analysis and its applications

Yoshida

2022

Stat Inference Stoch Process

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“…Jump filtering problems: jump diffusion processes Ogihara and Yoshida([18]), threshold estimation for stochastic processes with small noise (Shimizu [21]), global jump filters (Inatsugu and Yoshida [6]). Partial quasi-likelihood analysis: Yoshida [31]. Such variety of applications are demonstrating the universality of the framework of the QLA.…”

Section: Introductionmentioning

confidence: 99%

Simplified quasi-likelihood analysis for a locally asymptotically quadratic random field

Yoshida

2021

Preprint

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The asymptotic decision theory by Le Cam and Hajek has been given a lucid perspective by the Ibragimov-Hasminskii theory on convergence of the likelihood random field. Their scheme has been applied to stochastic processes by Kutoyants, and today this plot is called the IHK program. This scheme ensures that asymptotic properties of an estimator follow directly from the convergence of the random field if a large deviation estimate exists. The quasi-likelihood analysis (QLA) proved a polynomial type large deviation (PLD) inequality to go through a bottleneck of the program. A conclusion of the QLA is that if the quasi-likelihood random field is asymptotically quadratic and if a key index reflecting identifiability the random field has is non-degenerate, then the PLD inequality is always valid, and as a result, the IHK program can run. Many studies already took advantage of the QLA theory. However, not a few of them are using it in an inefficient way yet. The aim of this paper is to provide a reformed and simplified version of the QLA and to improve accessibility to the theory. As an example of the effects of the theory based on the PLD, the user can obtain asymptotic properties of the quasi-Bayesian estimator by only verifying non-degeneracy of a key index.

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Simplified quasi-likelihood analysis for a locally asymptotically quadratic random field

Yoshida

2024

Ann Inst Stat Math

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Partial quasi-likelihood analysis

Cited by 5 publications

References 32 publications

Quasi-likelihood analysis and its applications

Quasi-likelihood analysis and its applications

Simplified quasi-likelihood analysis for a locally asymptotically quadratic random field

Simplified quasi-likelihood analysis for a locally asymptotically quadratic random field

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