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

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  • Song, Kyungchul

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.

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  • Song, Kyungchul, 2014. "Local asymptotic minimax estimation of nonregular parameters with translation-scale equivariant maps," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 136-158.
    • Handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:136-158
    DOI: 10.1016/j.jmva.2013.10.020
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    References listed on IDEAS

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    1. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
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    Cited by:

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    3. Timothy B. Armstrong, 2014. "A Note on Minimax Testing and Confidence Intervals in Moment Inequality Models," Cowles Foundation Discussion Papers 1975, Cowles Foundation for Research in Economics, Yale University.
    4. Daido Kido, 2023. "Locally Asymptotically Minimax Statistical Treatment Rules Under Partial Identification," Papers 2311.08958, arXiv.org.
    5. Chen, Qihui & Fang, Zheng, 2019. "Inference on functionals under first order degeneracy," Journal of Econometrics, Elsevier, vol. 210(2), pages 459-481.

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