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Threshold Estimation for Stochastic Processes with Small Noise

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  • Yasutaka Shimizu

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  • 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.
    • Handle: RePEc:bla:scjsta:v:44:y:2017:i:4:p:951-988
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    File URL: http://hdl.handle.net/10.1111/sjos.12287
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    References listed on IDEAS

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    1. Uchida, Masayuki, 2008. "Approximate martingale estimating functions for stochastic differential equations with small noises," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1706-1721, September.
    2. 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.
    3. Akihiko Takahashi & Nakahiro Yoshida, 2004. "An Asymptotic Expansion Scheme for Optimal Investment Problems," Statistical Inference for Stochastic Processes, Springer, vol. 7(2), pages 153-188, May.
    4. Masayuki Uchida & Nakahiro Yoshida, 2004. "Asymptotic Expansion for Small Diffusions Applied to Option Pricing," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 189-223, October.
    5. Yasutaka Shimizu & Nakahiro Yoshida, 2006. "Estimation of Parameters for Diffusion Processes with Jumps from Discrete Observations," Statistical Inference for Stochastic Processes, Springer, vol. 9(3), pages 227-277, October.
    6. Gloter, Arnaud & Sørensen, Michael, 2009. "Estimation for stochastic differential equations with a small diffusion coefficient," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 679-699, March.
    7. Long, Hongwei, 2009. "Least squares estimator for discretely observed Ornstein-Uhlenbeck processes with small Lévy noises," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2076-2085, October.
    8. Naoto Kunitomo & Akihiko Takahashi, 2001. "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 117-151, January.
    9. Long, Hongwei & Shimizu, Yasutaka & Sun, Wei, 2013. "Least squares estimators for discretely observed stochastic processes driven by small Lévy noises," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 422-439.
    10. Yasutaka Shimizu, 2012. "Local asymptotic mixed normality for discretely observed non-recurrent Ornstein–Uhlenbeck processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 193-211, February.
    11. Ilya Pavlyukevich, 2008. "Ruin probabilities of small noise jump‐diffusions with heavy tails," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(1), pages 65-82, January.
    12. Yasutaka Shimizu, 2006. "M-Estimation for Discretely Observed Ergodic Diffusion Processes with Infinitely Many Jumps," Statistical Inference for Stochastic Processes, Springer, vol. 9(2), pages 179-225, July.
    13. Ma, Chunhua, 2010. "A note on "Least squares estimator for discretely observed Ornstein-Uhlenbeck processes with small Lévy noises"," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1528-1531, October.
    14. T. Ogihara & N. Yoshida, 2011. "Quasi-likelihood analysis for the stochastic differential equation with jumps," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 189-229, October.
    15. Masayuki Uchida, 2004. "Estimation for Discretely Observed Small Diffusions Based on Approximate Martingale Estimating Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 553-566, December.
    16. Yasutaka Shimizu, 2010. "Threshold selection in jump-discriminant filter for discretely observed jump processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 355-378, August.
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    Cited by:

    1. Mitsuki Kobayashi & Yasutaka Shimizu, 2023. "Threshold estimation for jump-diffusions under small noise asymptotics," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 361-411, July.

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