Robust Estimation of Some Nonregular Parameters

Kyungchul Song ()
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Kyungchul Song: Department of Economics, University of Pennsylvania

PIER Working Paper Archive from Penn Institute for Economic Research, 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.

Keywords: Local Asymptotic Minimax Estimation; Average Risks; Limit Experiments; Nondifferentiable Functionals; Partial Identification (search for similar items in EconPapers)
JEL-codes: C10 C13 C14 C44 (search for similar items in EconPapers)
Pages: 43 pages
Date: 2010-06-17
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (3)

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