IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v64y2012i5p991-1007.html
   My bibliography  Save this article

Some problems in nonparametric inference for the stress release process related to the local time

Author

Listed:
  • Takayuki Fujii
  • Yoichi Nishiyama

Abstract

This paper is concerned with nonparametric statistics for the stress release process. We propose the local time estimator (LTE) for the stationary density and show that it is unbiased and uniformly consistent. The LTE is used in constructing an estimator for the intensity function. A goodness of fit test for the intensity function is also presented. In these studies, the local time of the stress release process plays an important role. Copyright The Institute of Statistical Mathematics, Tokyo 2012

Suggested Citation

  • Takayuki Fujii & Yoichi Nishiyama, 2012. "Some problems in nonparametric inference for the stress release process related to the local time," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 991-1007, October.
    • Handle: RePEc:spr:aistmt:v:64:y:2012:i:5:p:991-1007
    DOI: 10.1007/s10463-011-0344-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-011-0344-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-011-0344-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yu. Kutoyants, 1998. "Efficient Density Estimation for Ergodic Diffusion Processes," Statistical Inference for Stochastic Processes, Springer, vol. 1(2), pages 131-155, May.
    2. Hayashi, T., 1986. "Laws of large numbers in self-correcting point processes," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 319-326, December.
    3. Ogata, Y. & Vere-Jones, D., 1984. "Inference for earthquake models: A self-correcting model," Stochastic Processes and their Applications, Elsevier, vol. 17(2), pages 337-347, July.
    4. Nobuo Inagaki & Toshihabu Hayashi, 1990. "Parameter estimation for the simple self-correcting point process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 89-98, March.
    5. Ilia Negri & Yoichi Nishiyama, 2009. "Goodness of fit test for ergodic diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 919-928, December.
    6. J. van Zanten, 2000. "On the Uniform Convergence of the Empirical Density of an Ergodic Diffusion," Statistical Inference for Stochastic Processes, Springer, vol. 3(3), pages 251-262, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nobuo Inagaki & Toshihabu Hayashi, 1990. "Parameter estimation for the simple self-correcting point process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 89-98, March.
    2. Maroua Ben Abdeddaiem, 2016. "On goodness-of-fit tests for parametric hypotheses in perturbed dynamical systems using a minimum distance estimator," Statistical Inference for Stochastic Processes, Springer, vol. 19(3), pages 259-287, October.
    3. Dalalyan Arnak S. & Kutoyants Yury A., 2004. "On second order minimax estimation of invariant density for ergodic diffusion," Statistics & Risk Modeling, De Gruyter, vol. 22(1), pages 17-42, January.
    4. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers math/0411034, arXiv.org.
    5. Zongwu Cai & Hongwei Mei & Rui Wang, 2024. "A model specification test for nonlinear stochastic diffusions with delay," Statistical Inference for Stochastic Processes, Springer, vol. 27(3), pages 795-812, October.
    6. M. Kleptsyna & Yu. Kutoyants, 2014. "On asymptotically distribution free tests with parametric hypothesis for ergodic diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 17(3), pages 295-319, October.
    7. Chen, Qiang & Zheng, Xu & Pan, Zhiyuan, 2015. "Asymptotically distribution-free tests for the volatility function of a diffusion," Journal of Econometrics, Elsevier, vol. 184(1), pages 124-144.
    8. F. Musmeci & D. Vere-Jones, 1992. "A space-time clustering model for historical earthquakes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 1-11, March.
    9. Estate V. Khmaladze, 2021. "How to test that a given process is an Ornstein–Uhlenbeck process," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 405-419, July.
    10. Su, Fei & Chan, Kung-Sik, 2015. "Quasi-likelihood estimation of a threshold diffusion process," Journal of Econometrics, Elsevier, vol. 189(2), pages 473-484.
    11. Yury Kutoyants, 2014. "On asymptotic distribution of parameter free tests for ergodic diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 17(2), pages 139-161, July.
    12. Frederic Schoenberg, 2002. "On Rescaled Poisson Processes and the Brownian Bridge," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 445-457, June.
    13. Ilia Negri & Yoichi Nishiyama, 2010. "Goodness of fit test for ergodic diffusions by tick time sample scheme," Statistical Inference for Stochastic Processes, Springer, vol. 13(1), pages 81-95, April.
    14. Ilia Negri & Yoichi Nishiyama, 2010. "Review on Goodness of Fit Tests for Ergodic Diffusion Processes by Different Sampling Schemes," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 39(1‐2), pages 91-106, February.
    15. Kristensen, Dennis, 2011. "Semi-nonparametric estimation and misspecification testing of diffusion models," Journal of Econometrics, Elsevier, vol. 164(2), pages 382-403, October.
    16. Ilia Negri & Li Zhou, 2014. "On goodness-of-fit testing for ergodic diffusion process with shift parameter," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 51-73, April.
    17. Zongwu Cai & Hongwei Mei & Rui Wang, 2024. "Model Specification Tests of Heterogenous Agent Models with Aggregate Shocks under Partial Information," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202405, University of Kansas, Department of Economics, revised Feb 2024.
    18. Negri, Ilia, 2001. "On efficient estimation of invariant density for ergodic diffusion processes," Statistics & Probability Letters, Elsevier, vol. 51(1), pages 79-85, January.
    19. Monsalve-Cobis, Abelardo & González-Manteiga, Wenceslao & Febrero-Bande, Manuel, 2011. "Goodness-of-fit test for interest rate models: An approach based on empirical processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3073-3092, December.
    20. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:aistmt:v:64:y:2012:i:5:p:991-1007. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.