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Maximal Uniform Convergence Rates In Parametric Estimation Problems

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  • Beckert, Walter
  • McFadden, Daniel L.

Abstract

This paper considers parametric estimation problems with independent, identically nonregularly distributed data. It focuses on rate efficiency, 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. These rates are shown to be attainable in general classes of parametric estimation problems.

Suggested Citation

  • Beckert, Walter & McFadden, Daniel L., 2010. "Maximal Uniform Convergence Rates In Parametric Estimation Problems," Econometric Theory, Cambridge University Press, vol. 26(2), pages 469-500, April.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:02:p:469-500_10
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    References listed on IDEAS

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    1. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    2. Harry J. Paarsch, 1994. "A Comparison of Estimators for Empirical Models of Auctions," Annals of Economics and Statistics, GENES, issue 34, pages 115-141.
    3. 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.
    4. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    5. 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.
    6. repec:cup:etheor:v:9:y:1993:i:1:p:1-18 is not listed on IDEAS
    7. Cosslett, Stephen R, 1987. "Efficiency Bounds for Distribution-free Estimators of the Binary," Econometrica, Econometric Society, vol. 55(3), pages 559-585, May.
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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

    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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