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Sharp large deviations for the log-likelihood ratio of an α-Brownian bridge

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  • Zhao, Shoujiang
  • Zhou, Yanping

Abstract

We studied the sharp large deviations for the log-likelihood ratio of an α-Brownian bridge. The full expansion of the tail probability for the log-likelihood ratio was obtained by using a change of measure.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:12:p:2750-2758
    DOI: 10.1016/j.spl.2013.06.003
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    References listed on IDEAS

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    1. 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.
    2. Bercu, Bernard & Coutin, Laure & Savy, Nicolas, 2012. "Sharp large deviations for the non-stationary Ornstein–Uhlenbeck process," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3393-3424.
    3. Pavel Gapeev & Uwe Küchler, 2008. "On large deviations in testing Ornstein–Uhlenbeck-type models," Statistical Inference for Stochastic Processes, Springer, vol. 11(2), pages 143-155, June.
    4. 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.
    5. Bishwal, Jaya P.N., 2008. "Large deviations in testing fractional Ornstein-Uhlenbeck models," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 953-962, June.
    6. Zhao, Shoujiang & Gao, Fuqing, 2010. "Large deviations in testing Jacobi model," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 34-41, January.
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    Cited by:

    1. Görgens, Maik & Thulin, Måns, 2014. "Bias-correction of the maximum likelihood estimator for the α-Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 78-86.
    2. Zhao, Shoujiang & Zhou, Qianqian, 2019. "On large deviation expansion for log-likelihood ratio of non-homogeneous Ornstein–Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    3. 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.

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