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

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  • Nakahiro Yoshida

    (University of Tokyo)

Abstract

The IHK program is a general framework in asymptotic decision theory, introduced by Ibragimov and Hasminskii and extended to semimartingales by Kutoyants. The quasi-likelihood analysis (QLA) asserts that a polynomial type large deviation inequality is always valid if the quasi-likelihood random field is asymptotically quadratic and if a key index reflecting the identifiability is non-degenerate. As a result, following the IHK program, the QLA gives a way to inference for various nonlinear stochastic processes. This paper provides a reformed and simplified version of the QLA and improves accessibility to the theory. As an example of the advantages of the scheme, the user can obtain asymptotic properties of the quasi-Bayesian estimator by only verifying non-degeneracy of the key index.

Suggested Citation

  • Nakahiro Yoshida, 2025. "Simplified quasi-likelihood analysis for a locally asymptotically quadratic random field," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(1), pages 1-24, February.
    • Handle: RePEc:spr:aistmt:v:77:y:2025:i:1:d:10.1007_s10463-024-00907-8
    DOI: 10.1007/s10463-024-00907-8
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    References listed on IDEAS

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    1. Nakahiro Yoshida, 2011. "Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 431-479, June.
    2. Yuta Umezu & Yusuke Shimizu & Hiroki Masuda & Yoshiyuki Ninomiya, 2019. "AIC for the non-concave penalized likelihood method," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 247-274, April.
    3. Masayuki Uchida, 2010. "Contrast-based information criterion for ergodic diffusion processes from discrete observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(1), pages 161-187, February.
    4. Yasutaka Shimizu, 2017. "Threshold Estimation for Stochastic Processes with Small Noise," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 951-988, December.
    5. Yusuke Shimizu, 2017. "Moment convergence of regularized least-squares estimator for linear regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1141-1154, October.
    6. Ogihara, Teppei & Yoshida, Nakahiro, 2014. "Quasi-likelihood analysis for nonsynchronously observed diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2954-3008.
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