IDEAS home Printed from https://ideas.repec.org/a/spr/sistpr/v21y2018i2d10.1007_s11203-018-9178-8.html
   My bibliography  Save this article

A review of asymptotic theory of estimating functions

Author

Listed:
  • Jean Jacod

    (Université P. et M. Curie (Paris-6))

  • Michael Sørensen

    (University of Copenhagen)

Abstract

Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic distribution are treated separately. Our conditions are not minimal, but can be verified for many interesting stochastic process models. Several examples illustrate the wide applicability of the theory and why the generality is needed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:21:y:2018:i:2:d:10.1007_s11203-018-9178-8
    DOI: 10.1007/s11203-018-9178-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11203-018-9178-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11203-018-9178-8?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. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Julie Lyng Forman & Michael Sørensen, 2008. "The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 438-465, September.
    3. 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.
    4. Uchida, Masayuki & Yoshida, Nakahiro, 2013. "Quasi likelihood analysis of volatility and nondegeneracy of statistical random field," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2851-2876.
    5. 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.
    6. Kuersteiner, Guido M., 2002. "Efficient Iv Estimation For Autoregressive Models With Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 18(3), pages 547-583, June.
    7. Hansen, Lars Peter, 1985. "A method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 203-238.
    8. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    9. Yuan, Ke-Hai & Jennrich, Robert I., 1998. "Asymptotics of Estimating Equations under Natural Conditions," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 245-260, May.
    10. Asger Roer Pedersen, 2000. "Estimating the Nitrous Oxide Emission Rate from the Soil Surface by Means of a Diffusion Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 385-403, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jakobsen, Nina Munkholt & Sørensen, Michael, 2019. "Estimating functions for jump–diffusions," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3282-3318.
    2. Frédéric Lavancier & Arnaud Poinas & Rasmus Waagepetersen, 2021. "Adaptive estimating function inference for nonstationary determinantal point processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 87-107, March.

    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. Stanislav Anatolyev, 2007. "Optimal Instruments In Time Series: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 143-173, February.
    2. Stefan Nagel, 2013. "Empirical Cross-Sectional Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 5(1), pages 167-199, November.
    3. Ai, Chunrong & Chen, Xiaohong, 2012. "The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions," Journal of Econometrics, Elsevier, vol. 170(2), pages 442-457.
    4. Xiaohong Chen & David Jacho-Chávez & Oliver Linton, 2012. "Averaging of moment condition estimators," CeMMAP working papers 26/12, Institute for Fiscal Studies.
    5. Kuersteiner, Guido M., 2001. "Optimal instrumental variables estimation for ARMA models," Journal of Econometrics, Elsevier, vol. 104(2), pages 359-405, September.
    6. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.
    7. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    8. Michael Sørensen, 2008. "Parametric inference for discretely sampled stochastic differential equations," CREATES Research Papers 2008-18, Department of Economics and Business Economics, Aarhus University.
    9. Carrasco, Marine & Florens, Jean-Pierre, 2014. "On The Asymptotic Efficiency Of Gmm," Econometric Theory, Cambridge University Press, vol. 30(2), pages 372-406, April.
    10. Kenneth West & Ka-fu Wong & Stanislav Anatolyev, 2009. "Instrumental Variables Estimation of Heteroskedastic Linear Models Using All Lags of Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 441-467.
    11. West, Kenneth D, 2001. "On Optimal Instrumental Variables Estimation of Stationary Time Series Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 1043-1050, November.
    12. Nour Meddahi & Eric Renault, 1998. "Quadratic M-Estimators for ARCH-Type Processes," CIRANO Working Papers 98s-29, CIRANO.
    13. Martyn Andrews & Obbey Elamin & Alastair R. Hall & Kostas Kyriakoulis & Matthew Sutton, 2017. "Inference in the presence of redundant moment conditions and the impact of government health expenditure on health outcomes in England," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 23-41, March.
    14. Christensen, Bent Jesper & Posch, Olaf & van der Wel, Michel, 2016. "Estimating dynamic equilibrium models using mixed frequency macro and financial data," Journal of Econometrics, Elsevier, vol. 194(1), pages 116-137.
    15. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2020. "The Efficiency Gap," Papers 2010.14146, arXiv.org, revised Sep 2022.
    16. Bruce N. Lehmann, 2005. "The Role of Beliefs in Inference for Rational Expectations Models," NBER Working Papers 11758, National Bureau of Economic Research, Inc.
    17. Hansen, Lars Peter & Heaton, John & Luttmer, Erzo G J, 1995. "Econometric Evaluation of Asset Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 237-274.
    18. Xiaohong Chen & Andres Santos, 2018. "Overidentification in Regular Models," Econometrica, Econometric Society, vol. 86(5), pages 1771-1817, September.
    19. Arthur Lewbel, 2012. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 67-80.
    20. Xiaohong Chen & Victor Chernozhukov & Sokbae Lee & Whitney K. Newey, 2014. "Local Identification of Nonparametric and Semiparametric Models," Econometrica, Econometric Society, vol. 82(2), pages 785-809, March.

    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:sistpr:v:21:y:2018:i:2:d:10.1007_s11203-018-9178-8. 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.