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Maximal Uniform Convergence Rates in Parametric Estimation Problems

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Author Info
Walter Beckert (Department of Economics, Mathematics & Statistics, Birkbeck)
Daniel McFadden

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Abstract

This paper considers parametric estimation problems with i.i.d. data. It focusses 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.

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File URL: http://www.ems.bbk.ac.uk/research/wp/PDF/BWPEF0405.pdf
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File Function: First version, 2004
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Publisher Info
Paper provided by Birkbeck, Department of Economics, Mathematics & Statistics in its series Birkbeck Working Papers in Economics and Finance with number 0405.

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Date of creation: Nov 2004
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Handle: RePEc:bbk:bbkefp:0405

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Related research
Keywords: parametric estimators; uniform convergence; Hellinger distance; Locally Asymptotically Quadratic (LAQ) Families;

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Econometric and Statistical Methods; Specific Distributions

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  1. repec:cup:etheor:v:9:y:1993:i:1:p:1-18 is not listed on IDEAS
  2. Paarsch, H.J., 1992. "A Comparison of estimators for Empirical Models of Auction," UWO Department of Economics Working Papers 9210, University of Western Ontario, Department of Economics.
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  3. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
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  4. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-67, July. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  6. 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(01), pages 1-18, January. [Downloadable!]
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