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Maximal uniform convergence rates in parametric estimation problems

Author

Listed:
  • Walter Beckert

    (Institute for Fiscal Studies and Birkbeck, University of London)

  • Daniel McFadden

    (Institute for Fiscal Studies and University of California, Berkeley)

Abstract

This paper considers parametric estimation problems with i.i.d. data. It focusses on rate-effciency, in the sense of maximal possible convergence rates of stochastically bounded estimators, as an optimality criterion, largely unexplored in parametric estimation. Under mild conditions, the Hellinger metric, defined on the space of parametric probability measures, is shown to be an essentially universally applicable tool to determine maximal possible convergence rates.

Suggested Citation

  • Walter Beckert & Daniel McFadden, 2005. "Maximal uniform convergence rates in parametric estimation problems," CeMMAP working papers CWP06/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:06/05
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    File URL: http://cemmap.ifs.org.uk/wps/cwp0605.pdf
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    References listed on IDEAS

    as
    1. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    2. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    3. Cosslett, Stephen R, 1987. "Efficiency Bounds for Distribution-free Estimators of the Binary," Econometrica, Econometric Society, vol. 55(3), pages 559-585, May.
    4. Harry J. Paarsch, 1994. "A Comparison of Estimators for Empirical Models of Auctions," Annals of Economics and Statistics, GENES, issue 34, pages 115-141.
    5. Horowitz, Joel L., 1993. "Optimal Rates of Convergence of Parameter Estimators in the Binary Response Model with Weak Distributional Assumptions," Econometric Theory, Cambridge University Press, vol. 9(1), pages 1-18, January.
    6. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    7. repec:cup:etheor:v:9:y:1993:i:1:p:1-18 is not listed on IDEAS
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    Cited by:

    1. McFadden, Daniel, 2022. "Instability in mixed logit demand models," Journal of choice modelling, Elsevier, vol. 43(C).

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    More about this item

    Keywords

    parametric estimators; uniform convergence; Hellinger distance; Locally Asymptotically Quadratic (LAQ) Families;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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