Local asymptotic minimax estimation of nonregular parameters with translation-scale equivariant maps

Kyungchul Song

Journal of Multivariate Analysis, 2014, vol. 125, issue C, 136-158

Abstract: When a parameter of interest is defined to be a nondifferentiable transform of a regular parameter, the parameter does not have an influence function, rendering the existing theory of semiparametric efficient estimation inapplicable. However, when the nondifferentiable transform is a known composite map of a continuous piecewise linear map with a single kink point and a translation-scale equivariant map, this paper demonstrates that it is possible to define a notion of asymptotic optimality of an estimator as an extension of the classical local asymptotic minimax estimation. This paper establishes a local asymptotic risk bound and proposes a general method to construct a local asymptotic minimax decision.

Keywords: Nonregular parameters; Translation-scale equivariant transforms; Semiparametric efficiency; Local asymptotic minimax estimation (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:125:y:2014:i:c:p:136-158

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DOI: 10.1016/j.jmva.2013.10.020

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