IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v125y2014icp136-158.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13002327
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmva.2013.10.020?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    2. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
    3. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    4. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
    5. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    6. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    7. van Eeden, Constance & Zidek, James V., 2004. "Combining the data from two normal populations to estimate the mean of one when their means difference is bounded," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 19-46, January.
    8. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Daido Kido, 2023. "Locally Asymptotically Minimax Statistical Treatment Rules Under Partial Identification," Papers 2311.08958, arXiv.org.
    2. Hiroaki Kaido & Yi Zhang, 2019. "Robust Likelihood Ratio Tests for Incomplete Economic Models," Papers 1910.04610, arXiv.org, revised Dec 2019.
    3. Hong, Han & Li, Jessie, 2018. "The numerical delta method," Journal of Econometrics, Elsevier, vol. 206(2), pages 379-394.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bulat Gafarov, 2019. "Simple subvector inference on sharp identified set in affine models," Papers 1904.00111, arXiv.org, revised Jul 2024.
    2. Semenova, Vira, 2023. "Debiased machine learning of set-identified linear models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1725-1746.
    3. Ho, Kate & Rosen, Adam M., 2015. "Partial Identification in Applied Research: Benefits and Challenges," CEPR Discussion Papers 10883, C.E.P.R. Discussion Papers.
    4. Tsunao Okumura & Emiko Usui, 2014. "Concave‐monotone treatment response and monotone treatment selection: With an application to the returns to schooling," Quantitative Economics, Econometric Society, vol. 5, pages 175-194, March.
    5. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2018. "Testing For A General Class Of Functional Inequalities," Econometric Theory, Cambridge University Press, vol. 34(5), pages 1018-1064, October.
    6. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    7. Vira Semenova, 2023. "Debiased Machine Learning of Aggregated Intersection Bounds and Other Causal Parameters," Papers 2303.00982, arXiv.org, revised May 2025.
    8. Chesher, Andrew & Rosen, Adam M., 2020. "Generalized instrumental variable models, methods, and applications," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 1-110, Elsevier.
    9. Molinari, Francesca, 2020. "Microeconometrics with partial identification," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 355-486, Elsevier.
    10. Hiroaki Kaido & Jiaxuan Li & Marc Rysman, 2018. "Moment Inequalities in the Context of Simulated and Predicted Variables," Papers 1804.03674, arXiv.org.
    11. Kyungchul Song, 2009. "Point Decisions for Interval-Identified Parameters," PIER Working Paper Archive 09-036, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    12. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. Andrew Chesher & Adam Rosen, 2015. "Characterizations of identified sets delivered by structural econometric models," CeMMAP working papers CWP63/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Jiannan Lu & Peng Ding & Tirthankar Dasgupta, 2018. "Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds," Journal of Educational and Behavioral Statistics, , vol. 43(5), pages 540-567, October.
    15. Vikesh Amin & Jere R. Behrman & Jason M. Fletcher & Carlos A. Flores & Alfonso Flores-Lagunes & Hans-Peter Kohler, 2022. "Does Schooling Improve Cognitive Abilities at Older Ages: Causal Evidence from Nonparametric Bounds," PIER Working Paper Archive 22-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    16. repec:osf:socarx:bwxfz_v1 is not listed on IDEAS
    17. Qian, Hang, 2011. "Bayesian inference with monotone instrumental variables," MPRA Paper 32672, University Library of Munich, Germany.
    18. Joachim Freyberger & Bradley J. Larsen, 2025. "How Well Does Bargaining Work in Consumer Markets? A Robust Bounds Approach," Econometrica, Econometric Society, vol. 93(1), pages 161-194, January.
    19. Lukáš Lafférs, 2019. "Identification in Models with Discrete Variables," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 657-696, February.
    20. repec:cwl:cwldpp:1761rr is not listed on IDEAS
    21. Ivan A. Canay & Azeem M. Shaikh, 2016. "Practical and theoretical advances in inference for partially identified models," CeMMAP working papers 05/16, Institute for Fiscal Studies.
    22. Lina Zhang & David T. Frazier & D.S. Poskitt & Xueyan Zhao, 2025. "Decomposing identification gains and evaluating instrument identification power for partially identified average treatment effects," Econometric Reviews, Taylor & Francis Journals, vol. 44(7), pages 915-938, August.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:136-158. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.