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Robust Estimation of Some Nonregular Parameters

Author

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  • Kyungchul Song

    (Department of Economics, University of Pennsylvania)

Abstract

This paper develops optimal estimation of a potentially nondifferentiable functional Г(β) of a regular parameter β, when Г satisfies certain conditions. Primary examples are min or max functionals that frequently appear in the analysis of partially identified models. This paper investigates both the average risk approach and the minimax approach. The average risk approach considers average local asymptotic risk with a weight function Πover β-q(β) for a fixed location-scale equivariant map q, and the minimax approach searches for a robust decision that minimizes the local asymptotic maximal risk. In both approaches, optimal decisions are proposed. Certainly, the average risk approach is preferable to the minimax approach when one has fairly accurate information of β-q(β). When one does not, one may ask whether the average risk decision with a certain weight function Πis as robust as the minimax decision. This paper specifies conditions for Г such that the answer is negative. This paper discusses some results from Monte Carlo simulation studies.

Suggested Citation

  • Kyungchul Song, 2010. "Robust Estimation of Some Nonregular Parameters," PIER Working Paper Archive 10-020, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:10-020
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    Cited by:

    1. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1218-1241, October.

    More about this item

    Keywords

    Local Asymptotic Minimax Estimation; Average Risks; Limit Experiments; Nondifferentiable Functionals; Partial Identification;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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