IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v66y2004i3p335-345.html
   My bibliography  Save this article

Efficient estimators for functionals of Markov chains with parametric marginals

Author

Listed:
  • Penev, Spiridon
  • Peng, Hanxiang
  • Schick, Anton
  • Wefelmeyer, Wolfgang

Abstract

Suppose we observe a geometrically ergodic Markov chain with a parametric model for the marginal, but no (further) information about the transition distribution. Then the empirical estimator for a linear functional of the joint law of two successive observations is no longer efficient. We construct an improved estimator and show that it is efficient. The construction is similar to a recent one for bivariate models with parametric marginals. The result applies to discretely observed parametric continuous-time processes.

Suggested Citation

  • Penev, Spiridon & Peng, Hanxiang & Schick, Anton & Wefelmeyer, Wolfgang, 2004. "Efficient estimators for functionals of Markov chains with parametric marginals," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 335-345, February.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:3:p:335-345
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00361-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Bo Martin Bibby & Michael Sørensen, 2001. "Simplified Estimating Functions for Diffusion Models with a High‐dimensional Parameter," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 99-112, March.
    2. Mathieu Kessler, 2000. "Simple and Explicit Estimating Functions for a Discretely Observed Diffusion Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 65-82, March.
    3. Peng, Hanxiang & Schick, Anton, 2002. "On efficient estimation of linear functionals of a bivariate distribution with known marginals," Statistics & Probability Letters, Elsevier, vol. 59(1), pages 83-91, August.
    4. Glynn, Peter W. & Ormoneit, Dirk, 2002. "Hoeffding's inequality for uniformly ergodic Markov chains," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 143-146, January.
    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. Weiwei Guo & Lingfei Li, 2019. "Parametric inference for discretely observed subordinate diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 22(1), pages 77-110, April.
    2. J. Jimenez & R. Biscay & T. Ozaki, 2005. "Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(2), pages 109-141, June.
    3. Friedrich Hubalek & Petra Posedel, 2008. "Asymptotic analysis for a simple explicit estimator in Barndorff-Nielsen and Shephard stochastic volatility models," Papers 0807.3479, arXiv.org.
    4. Jean Jacod & Michael Sørensen, 2018. "A review of asymptotic theory of estimating functions," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 415-434, July.
    5. Kusuoka, Seiichiro & Tudor, Ciprian A., 2012. "Stein’s method for invariant measures of diffusions via Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1627-1651.
    6. H. S. Chang, 2004. "Technical Note: On Ordinal Comparison of Policies in Markov Reward Processes," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 207-217, July.
    7. A. M. Kulik & N. N. Leonenko & I. Papić & N. Šuvak, 2020. "Parameter Estimation for Non-Stationary Fisher-Snedecor Diffusion," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1023-1061, September.
    8. Yongqiang Tang, 2007. "A Hoeffding-Type Inequality for Ergodic Time Series," Journal of Theoretical Probability, Springer, vol. 20(2), pages 167-176, June.
    9. Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations. Working paper #2," NCER Working Paper Series 2, National Centre for Econometric Research.
    10. Aliu, A. Hassan & Abiodun A. A. & Ipinyomi R.A., 2017. "Statistical Inference for Discretely Observed Diffusion Epidemic Models," International Journal of Mathematics Research, Conscientia Beam, vol. 6(1), pages 29-35.
    11. Ahmad, I.A. & Amezziane, M., 2013. "Probability inequalities for bounded random vectors," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1136-1142.
    12. Peng Hanxiang & Schick Anton, 2004. "Estimation of linear functionals of bivariate distributions with parametric marginals," Statistics & Risk Modeling, De Gruyter, vol. 22(1), pages 61-78, January.
    13. Liu, Jinpeng & Liu, Yuanyuan & Zhao, Yiqiang Q., 2022. "Augmented truncation approximations to the solution of Poisson’s equation for Markov chains," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    14. A. S. Hurn & J. I. Jeisman & K. A. Lindsay, 0. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 390-455.
    15. Andreas Neuenkirch & Samy Tindel, 2014. "A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 99-120, April.
    16. Friedrich Hubalek & Petra Posedel, 2011. "Joint analysis and estimation of stock prices and trading volume in Barndorff-Nielsen and Shephard stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 11(6), pages 917-932.
    17. Shie Mannor & John N. Tsitsiklis, 2005. "On the Empirical State-Action Frequencies in Markov Decision Processes Under General Policies," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 545-561, August.
    18. Hunt, F.Y., 2005. "Sample path optimality for a Markov optimization problem," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 769-779, May.
    19. Alessandro Gregorio & Stefano Iacus, 2008. "Parametric estimation for the standard and geometric telegraph process observed at discrete times," Statistical Inference for Stochastic Processes, Springer, vol. 11(3), pages 249-263, October.
    20. Peng, Hanxiang & Schick, Anton, 2005. "Efficient estimation of linear functionals of a bivariate distribution with equal, but unknown marginals: the least-squares approach," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 385-409, August.

    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:eee:stapro:v:66:y:2004:i:3:p:335-345. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.