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Robust and efficient parameter estimation for discretely observed stochastic processes

Author

Listed:
  • Rohan Hore

    (University of Chicago)

  • Abhik Ghosh

    (Indian Statistical Institute)

Abstract

In various practical situations, we encounter data from stochastic processes which can be efficiently modeled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, maximum likelihood (ML) estimation, the most common approach, is sensitive to slight model deviations or data contamination due to its well-known lack of robustness. Since the non-parametric alternatives often sacrifice efficiency, in this paper we develop a robust parameter estimation procedure for discretely observed data from a parametric stochastic process model which exploits the nice properties of the popular density power divergence measure. In particular, here we define the minimum density power divergence estimators (MDPDE) for the independent increment and the Markov processes. We establish the asymptotic consistency and distributional results for the proposed MDPDEs in these dependent stochastic process setups and illustrate their benefits over the usual ML estimator for common examples like the Poisson process, drifted Brownian motion and the auto-regressive models.

Suggested Citation

  • Rohan Hore & Abhik Ghosh, 2025. "Robust and efficient parameter estimation for discretely observed stochastic processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(3), pages 387-424, June.
    • Handle: RePEc:spr:aistmt:v:77:y:2025:i:3:d:10.1007_s10463-024-00922-9
    DOI: 10.1007/s10463-024-00922-9
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    References listed on IDEAS

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    1. Jin‐Hong Park & T. N. Sriram, 2017. "Robust estimation of conditional variance of time series using density power divergences," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(6), pages 703-717, September.
    2. Byungsoo Kim & Sangyeol Lee, 2020. "Robust estimation for general integer-valued time series models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1371-1396, December.
    3. Kim, Byungsoo & Lee, Sangyeol, 2013. "Robust estimation for the covariance matrix of multivariate time series based on normal mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 125-140.
    4. Andrews T. Anum & Michael Pokojovy, 2024. "A hybrid method for density power divergence minimization with application to robust univariate location and scale estimation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(14), pages 5186-5209, April.
    5. Genton, Marc G. & Ma, Yanyuan, 1999. "Robustness properties of dispersion estimators," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 343-350, October.
    6. Nakahiro Yoshida & Toshiharu Hayashi, 1990. "On the robust estimation in poisson processes with periodic intensities," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(3), pages 489-507, September.
    7. Weems, K. S. & Smith, P. J., 2004. "On robustness of maximum likelihood estimates for Poisson-lognormal models," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 189-196, January.
    8. Abhik Ghosh, 2022. "Robust parametric inference for finite Markov chains," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 118-147, March.
    9. Kulkarni, P.M. & Heyde, C.C., 1987. "Optimal robust estimation for discrete time stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 267-276.
    10. Abhik Ghosh & Ayanendranath Basu, 2015. "Robust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 2056-2072, September.
    11. Nakahiro Yoshida, 1988. "Robust M-estimators in diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 799-820, December.
    12. Sonja Rieder, 2012. "Robust parameter estimation for the Ornstein–Uhlenbeck process," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 411-436, November.
    13. Kang, Jiwon & Lee, Sangyeol, 2014. "Minimum density power divergence estimator for Poisson autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 44-56.
    14. Renato Assunção & Peter Guttorp, 1999. "Robustness for Inhomogeneous Poisson Point Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(4), pages 657-678, December.
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