IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v72y1997i1p27-45.html
   My bibliography  Save this article

On asymptotically optimal estimates for general observations

Author

Listed:
  • Vajda, Igor
  • Janzura, Martin

Abstract

Asymptotically maximum likelihood estimators and estimators asymptotically minimizing criterial functions of observations are considered in statistical models with generalized sequences of observations. New necessary and sufficient conditions for consistency of these estimators are established. The applicability of these conditions is illustrated on regression models with Gaussian and contaminated observations and on models of exponentially distributed random processes and fields.

Suggested Citation

  • Vajda, Igor & Janzura, Martin, 1997. "On asymptotically optimal estimates for general observations," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 27-45, December.
    • Handle: RePEc:eee:spapps:v:72:y:1997:i:1:p:27-45
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00082-3
    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. Liese, F. & Vajda, I., 1994. "Consistency of M-Estimates in General Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 93-114, July.
    2. Vajda, Igor, 1995. "Conditions equivalent to consistency of approximate MLE's for stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 35-56, March.
    3. Friedrich Liese & Igor Vajda, 1995. "Necessary and sufficient conditions for consistency of generalizedM-estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 291-324, December.
    4. Luschgy Harald, 1993. "Second Order Behavior Of Neyman-Pearson Tests For Stochastic Processes," Statistics & Risk Modeling, De Gruyter, vol. 11(2), pages 133-150, February.
    5. DRYGAS, Hilmar, 1976. "Weak and strong consistency of the least squares estimators in regression models," LIDAM Reprints CORE 236, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Yannis Yatracos, 2006. "On Consistent Statistical Procedures in Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 379-387, June.
    2. Liebscher, Eckhard, 2003. "Strong convergence of estimators in nonlinear autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 247-261, February.
    3. Norbert Christopeit & Michael Massmann, 2013. "A Note on an Estimation Problem in Models with Adaptive Learning," Tinbergen Institute Discussion Papers 13-151/III, Tinbergen Institute.
    4. Bantli, Faouzi El & Hallin, Marc, 1999. "L1-estimation in linear models with heterogeneous white noise," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 305-315, December.
    5. Lita da Silva, João, 2014. "Some strong consistency results in stochastic regression," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 220-226.
    6. Bai, Z. D. & Guo, Meihui, 1999. "A paradox in least-squares estimation of linear regression models," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 167-174, April.
    7. Søren Johansen & Bent Nielsen, 2016. "Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 321-348, June.
    8. Spodarev, Evgeny & Straka, Peter & Winter, Steffen, 2015. "Estimation of fractal dimension and fractal curvatures from digital images," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 134-152.
    9. Friedrich Liese & Igor Vajda, 1995. "Necessary and sufficient conditions for consistency of generalizedM-estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 291-324, December.
    10. Cohen, Guy & Francos, Joseph M., 2002. "Linear Least Squares Estimation of Regression Models for Two-Dimensional Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 431-444, August.
    11. Søren Johansen & Bent Nielsen, 2014. "Optimal hedging with the cointegrated vector autoregressive model," Discussion Papers 14-23, University of Copenhagen. Department of Economics.
    12. Guus Balkema & Paul Embrechts, 2018. "Linear Regression for Heavy Tails," Risks, MDPI, vol. 6(3), pages 1-70, September.
    13. Søren Johansen & Bent Nielsen, 2014. "Outlier detection algorithms for least squares time series regression," Economics Papers 2014-W04, Economics Group, Nuffield College, University of Oxford.
    14. Wu, Tiee-Jian & Wasan, M. T., 1996. "Weighted least squares estimates in linear regression models for processes with uncorrelated increments," Stochastic Processes and their Applications, Elsevier, vol. 64(2), pages 273-286, November.
    15. A. Mayoral & D. Morales & J. Morales & I. Vajda, 2003. "On efficiency of estimation and testing with data quantized to fixed number of cells," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 57(1), pages 1-27, February.
    16. Jun Shao, 1992. "Jackknifing in generalized linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(4), pages 673-686, December.
    17. Petr Lachout & Eckhard Liebscher & Silvia Vogel, 2005. "Strong convergence of estimators as ε n -minimisers of optimisation problemsof optimisation problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 291-313, June.

    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:spapps:v:72:y:1997:i:1:p:27-45. 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/505572/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.