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On the large deviation principle for maximum likelihood estimator of α-Brownian bridge

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  • Zhao, Shoujiang
  • Liu, Qiaojing
  • Chen, Ting

Abstract

We consider the large deviation principle for maximum likelihood estimator of α-Brownian bridge. The full large deviation with explicit rate function is obtained in the case of non-Gaussian limit distribution by local large deviation principle and exponential tightness.

Suggested Citation

  • Zhao, Shoujiang & Liu, Qiaojing & Chen, Ting, 2018. "On the large deviation principle for maximum likelihood estimator of α-Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 143-150.
    • Handle: RePEc:eee:stapro:v:138:y:2018:i:c:p:143-150
    DOI: 10.1016/j.spl.2018.03.001
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    References listed on IDEAS

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    1. Mark Trede & Bernd Wilfling, 2007. "Estimating exchange rate dynamics with diffusion processes: an application to Greek EMU data," Empirical Economics, Springer, vol. 33(1), pages 23-39, July.
    2. Zhao, Shoujiang & Zhou, Yanping, 2013. "Sharp large deviations for the log-likelihood ratio of an α-Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2750-2758.
    3. Bercu, Bernard & Richou, Adrien, 2017. "Large deviations for the Ornstein–Uhlenbeck process without tears," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 45-55.
    4. Brennan, Michael J & Schwartz, Eduardo S, 1990. "Arbitrage in Stock Index Futures," The Journal of Business, University of Chicago Press, vol. 63(1), pages 7-31, January.
    5. Shoujiang Zhao & Ting Chen, 2017. "Large deviation expansion for maximum-likelihood estimator of α −Brownian bridge," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(15), pages 7313-7326, August.
    6. David Sondermann & Mark Trede & Bernd Wilfling, 2011. "Estimating the degree of interventionist policies in the run-up to EMU," Applied Economics, Taylor & Francis Journals, vol. 43(2), pages 207-218.
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    Cited by:

    1. Zhao, Shoujiang & Liu, Qiaojing, 2020. "A large deviation result for maximum likelihood estimator of non-homogeneous Ornstein–Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 162(C).

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