IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v61y2020i1d10.1007_s00362-017-0928-2.html
   My bibliography  Save this article

Consistency of MLE, LSE and M-estimation under mild conditions

Author

Listed:
  • Jin Zhang

    (Yunnan University)

Abstract

Consistency of estimation is a necessary and essential asymptotic property, but consistency of MLE, LSE and M-estimation remains unsolved satisfactorily in the general case. A commonly used “standard condition” is shown to be almost false. A unified mild condition of consistency is established in this paper, and it is often a sufficient and necessary condition.

Suggested Citation

  • Jin Zhang, 2020. "Consistency of MLE, LSE and M-estimation under mild conditions," Statistical Papers, Springer, vol. 61(1), pages 189-199, February.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:1:d:10.1007_s00362-017-0928-2
    DOI: 10.1007/s00362-017-0928-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-017-0928-2
    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/s00362-017-0928-2?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. Lai, T. L. & Robbins, Herbert & Wei, C. Z., 1979. "Strong consistency of least squares estimates in multiple regression II," Journal of Multivariate Analysis, Elsevier, vol. 9(3), pages 343-361, September.
    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. R. M. Balan & Ioana Schiopu-Kratina, 2004. "Asymptotic Results with Generalized Estimating Equations for Longitudinal data II," RePAd Working Paper Series lrsp-TRS398, Département des sciences administratives, UQO.
    2. 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.
    3. Yuan-chin Chang, 2011. "Sequential estimation in generalized linear models when covariates are subject to errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(1), pages 93-120, January.
    4. Zhou, Xian & You, Jinhong, 2004. "Wavelet estimation in varying-coefficient partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 91-104, June.
    5. Yong Tao & Xiangjun Wu & Tao Zhou & Weibo Yan & Yanyuxiang Huang & Han Yu & Benedict Mondal & Victor M. Yakovenko, 2019. "Exponential structure of income inequality: evidence from 67 countries," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(2), pages 345-376, June.
    6. Li, Gaorong & Feng, Sanying & Peng, Heng, 2011. "A profile-type smoothed score function for a varying coefficient partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 372-385, February.
    7. 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.
    8. Norbert Christopeit & Michael Massmann, 2010. "Consistent Estimation of Structural Parameters in Regression Models with Adaptive Learning," Tinbergen Institute Discussion Papers 10-077/4, Tinbergen Institute.
    9. Arnoud V. den Boer & Bert Zwart, 2014. "Simultaneously Learning and Optimizing Using Controlled Variance Pricing," Management Science, INFORMS, vol. 60(3), pages 770-783, March.
    10. Li, Gaorong & Lin, Lu & Zhu, Lixing, 2012. "Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 85-111.
    11. Velilla, Santiago, 2001. "On the bootstrap in misspecified regression models," Computational Statistics & Data Analysis, Elsevier, vol. 36(2), pages 227-242, April.
    12. repec:cte:wsrepe:6351 is not listed on IDEAS
    13. Hans-Georg Müller & Chun-Lung Su & Stephen R. Dueker & Yumei Lin & Andrew Clifford & Bruce A. Buchholz & John S. Vogel, 2002. "Semiparametric Modeling of Labeled-Cell Kinetics, with Application to Isotope Labeling of Erythrocytes," Biometrics, The International Biometric Society, vol. 58(4), pages 937-945, December.
    14. den Boer, A.V., 2013. "Does adding data always improve linear regression estimates?," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 829-835.
    15. Ching-Kang Ing & Ching-Zong Wei, 2005. "A maximal moment inequality for long range dependent time series with applications to estimation and model selection," Econometrics 0508009, University Library of Munich, Germany.
    16. Zimu Chen & Zhanfeng Wang & Yuan‐chin Ivan Chang, 2020. "Sequential adaptive variables and subject selection for GEE methods," Biometrics, The International Biometric Society, vol. 76(2), pages 496-507, June.
    17. Lita da Silva, João, 2014. "Some strong consistency results in stochastic regression," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 220-226.
    18. Eck, Daniel J., 2018. "Bootstrapping for multivariate linear regression models," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 141-149.
    19. 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.
    20. Robin C. O. Palmberg & Yusak O. Susilo & Győző Gidófalvi & Fatemeh Naqavi, 2021. "Built Environment Characteristics, Daily Travel, and Biometric Readings: Creation of an Experimental Tool Based on a Smartwatch Platform," Sustainability, MDPI, vol. 13(17), pages 1-21, September.
    21. You, Jinhong & Chen, Gemai, 2006. "Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 324-341, February.

    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:stpapr:v:61:y:2020:i:1:d:10.1007_s00362-017-0928-2. 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.