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Maximal uniform convergence rates in parametric estimation problems

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  • Walter Beckert
  • 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.

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File URL: http://cemmap.ifs.org.uk/wps/cwp0605.pdf
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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP06/05.

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Length: 20 pp.
Date of creation: Jun 2005
Date of revision:
Handle: RePEc:ifs:cemmap:06/05

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Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
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Web page: http://cemmap.ifs.org.uk
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Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
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Related research

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

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  1. Bruce E. Hansen, 1996. "Sample Splitting and Threshold Estimation," Boston College Working Papers in Economics 319., Boston College Department of Economics, revised 12 May 1998.
  2. 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.
  3. Harry J. PAARSCH, 1994. "A Comparison of Estimators for Empirical Models of Auctions," Annales d'Economie et de Statistique, ENSAE, issue 34, pages 143-157.
  4. 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.
  5. repec:cup:etheor:v:9:y:1993:i:1:p:1-18 is not listed on IDEAS
  6. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-67, July.
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