IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v67y1998i2p349-366.html
   My bibliography  Save this article

More Higher-Order Efficiency: Concentration Probability

Author

Listed:
  • Kano, Yutaka

Abstract

Based on concentration probability of estimators about a true parameter, third-order asymptotic efficiency of the first-order bias-adjusted MLE within the class of first-order bias-adjusted estimators has been well established in a variety of probability models. In this paper we consider the class of second-order bias-adjusted Fisher consistent estimators of a structural parameter vector on the basis of an i.i.d. sample drawn from a curved exponential-type distribution, and study the asymptotic concentration probability, about a true parameter vector, of these estimators up to the fifth-order. In particular, (i) we show that third-order efficient estimators are always fourth-order efficient; (ii) a necessary and sufficient condition for fifth-order efficiency is provided; and finally (iii) the MLE is shown to be fifth-order efficient.

Suggested Citation

  • Kano, Yutaka, 1998. "More Higher-Order Efficiency: Concentration Probability," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 349-366, November.
    • Handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:349-366
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(98)91770-5
    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. Magnus, J.R. & Neudecker, H., 1985. "Matrix differential calculus with applications to simple, Hadamard, and Kronecker products," Other publications TiSEM 1b2f1740-bfd1-4ea5-986c-9, Tilburg University, School of Economics and Management.
    2. Masanobu Taniguchi, 1987. "Third Order Asymptotic Properties Of Blue And Lse For A Regression Model With Arma Residual," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(1), pages 111-114, January.
    3. Taniguchi, Masanobu, 1986. "Third order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 18(1), pages 1-31, February.
    4. Pfanzagl, J. & Wefelmeyer, W., 1978. "A third-order optimum property of the maximum likelihood estimator," Journal of Multivariate Analysis, Elsevier, vol. 8(1), pages 1-29, March.
    5. Dehling, Herold & Denker, Manfred & Woyczynski, Wojbor A., 1990. "Resampling U-statistics using p-stable laws," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 1-13, July.
    6. Takeuchi, Kei & Morimune, Kimio, 1985. "Third-Order Efficiency of the Extended Maximum Likelihood Estimators in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 53(1), pages 177-200, January.
    7. Rao C. R. & Sinha Β. K. & Subramanyam K., 1982. "Third Order Efficiency Of The Maximum Likelihood Estimator In The Multinomial Distribution," Statistics & Risk Modeling, De Gruyter, vol. 1(1), pages 1-16, January.
    8. Takeuchi, Mikitoshi, 1981. "Indian Monetary Policy and the Gold Exchange Standard," Economic Review, Hitotsubashi University, vol. 32(2), pages 97-109, April.
    9. Yuzo Hosoya, 1990. "Information amount and higher-order efficiency in estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 37-49, March.
    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. Kunitomo, Naoto & Matsushita, Yukitoshi, 2009. "Asymptotic expansions and higher order properties of semi-parametric estimators in a system of simultaneous equations," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1727-1751, September.
    2. Srivastava, V. K. & Maekawa, Koichi, 1995. "Efficiency properties of feasible generalized least squares estimators in SURE models under non-normal disturbances," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 99-121.
    3. Kundhi, Gubhinder & Rilstone, Paul, 2012. "Edgeworth expansions for GEL estimators," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 118-146.
    4. Jinyong Hahn & David W. Hughes & Guido Kuersteiner & Whitney K. Newey, 2024. "Efficient bias correction for cross‐section and panel data," Quantitative Economics, Econometric Society, vol. 15(3), pages 783-816, July.
    5. Mehmet Caner, 2005. "Nearly Singular design in gmm and generalized empirical likelihood estimators," Working Paper 211, Department of Economics, University of Pittsburgh, revised Jan 2005.
    6. Jeffrey M. Wooldridge, 2004. "Estimating average partial effects under conditional moment independence assumptions," CeMMAP working papers CWP03/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    8. Caner, Mehmet, 2008. "Nearly-singular design in GMM and generalized empirical likelihood estimators," Journal of Econometrics, Elsevier, vol. 144(2), pages 511-523, June.
    9. Victor Chernozhukov & Carlos Cinelli & Whitney Newey & Amit Sharma & Vasilis Syrgkanis, 2021. "Long Story Short: Omitted Variable Bias in Causal Machine Learning," Papers 2112.13398, arXiv.org, revised May 2024.
    10. Anat Bracha & Donald Brown, 2013. "(Ir)rational Exuberance: Optimism, Ambiguity, and Risk," Levine's Working Paper Archive 786969000000000782, David K. Levine.
    11. repec:hal:spmain:info:hdl:2441/f6h8764enu2lskk9p2m9mgp8l is not listed on IDEAS
    12. Kunitomo, N. & McAleer, M.J. & Nishiyama, Y., 2010. "Moment Restriction-based Econometric Methods: An Overview," Econometric Institute Research Papers EI 2010-61, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    13. Oya, Kosuke & Morimune, Kimio, 1992. "The distribution of the full information maximum likelihood estimator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 33(5), pages 569-574.
    14. Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December.
    15. Masanobu Taniguchi & Madan Puri, 1995. "Higher order asymptotic theory for normalizing transformations of maximum likelihood estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 581-600, September.
    16. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 991-1030.
    17. Michael Creel & Dennis Kristensen, "undated". "Indirect Likelihood Inference," Working Papers 558, Barcelona School of Economics.
    18. Michael Creel & Dennis Kristensen, 2013. "Indirect Likelihood Inference (revised)," UFAE and IAE Working Papers 931.13, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    19. Caro-Lopera, Francisco J. & Leiva, Víctor & Balakrishnan, N., 2012. "Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 126-139, February.
    20. Magnus, Jan R., 2010. "On the concept of matrix derivative," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2200-2206, October.
    21. Kyoo il Kim, 2006. "Higher Order Bias Correcting Moment Equation for M-Estimation and its Higher Order Efficiency," Labor Economics Working Papers 22453, East Asian Bureau of Economic Research.

    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:jmvana:v:67:y:1998:i:2:p:349-366. 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.