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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.

Suggested Citation

  • 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:

    1. Hiroaki Kaido & Yi Zhang, 2019. "Robust Likelihood Ratio Tests for Incomplete Economic Models," Papers 1910.04610, arXiv.org, revised Dec 2019.
    2. Hong, Han & Li, Jessie, 2018. "The numerical delta method," Journal of Econometrics, Elsevier, vol. 206(2), pages 379-394.
    3. Daido Kido, 2023. "Locally Asymptotically Minimax Statistical Treatment Rules Under Partial Identification," Papers 2311.08958, arXiv.org.
    4. Chen, Qihui & Fang, Zheng, 2019. "Inference on functionals under first order degeneracy," Journal of Econometrics, Elsevier, vol. 210(2), pages 459-481.
    5. 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.

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