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Uniform Inference in Nonlinear Models with Mixed Identification Strength

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  • Xu Cheng

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    (Department of Economics, University of Pennsylvania)

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    Abstract

    The paper studies inference in nonlinear models where identification loss presents in multiple parts of the parameter space. For uniform inference, we develop a local limit theory that models mixed identification strength. Building on this non-standard asymptotic approximation, we suggest robust tests and confidence intervals in the presence of non-identified and weakly identified nuisance parameters. In particular, this covers applications where some nuisance parameters are non-identified under the null (Davies (1977, 1987)) and some nuisance parameters are subject to a full range of identification strength. The asymptotic results involve both inconsistent estimators that depend on a localization parameter and consistent estimators with different rates of convergence. A sequential argument is used to peel the criterion function based on identification strength of the parameters. The robust test is uniformly valid and non-conservative.

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    File URL: http://economics.sas.upenn.edu/system/files/14-018.pdf
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    Bibliographic Info

    Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 14-018.

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    Length: 54 pages
    Date of creation: 08 May 2014
    Date of revision:
    Handle: RePEc:pen:papers:14-018

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    Related research

    Keywords: Mixed rates; nonlinear regression; robust inference; uniformity; weak identification.;

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