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Maximal uniform convergence rates in parametric estimation problems

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Author Info
Walter Beckert () (Institute for Fiscal Studies and Birkbeck College London)
Daniel McFadden () (Institute for Fiscal Studies and University of California, Berkeley)

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Abstract

This paper considers parametric estimation problems with independent, identically,non-regularly distributed data. It focuses 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. These rates are shown to be attainable in general classes of parametric estimation problems.

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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP28/07.

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Date of creation: Nov 2007
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Handle: RePEc:ifs:cemmap:28/07

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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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References listed on IDEAS
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  1. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
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  2. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-67, July. [Downloadable!] (restricted)
  3. 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)
  4. repec:cup:etheor:v:9:y:1993:i:1:p:1-18 is not listed on IDEAS
  5. 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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  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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