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• W2952004221 abstract "This paper studies an asymptotic framework for conducting inference on parameters of the form $phi(theta_0)$, where $phi$ is a known directionally differentiable function and $theta_0$ is estimated by $hat theta_n$. In these settings, the asymptotic distribution of the plug-in estimator $phi(hat theta_n)$ can be readily derived employing existing extensions to the Delta method. We show, however, that the standard bootstrap is only consistent under overly stringent conditions -- in particular we establish that differentiability of $phi$ is a necessary and sufficient condition for bootstrap consistency whenever the limiting distribution of $hat theta_n$ is Gaussian. An alternative resampling scheme is proposed which remains consistent when the bootstrap fails, and is shown to provide local size control under restrictions on the directional derivative of $phi$. We illustrate the utility of our results by developing a test of whether a Hilbert space valued parameter belongs to a convex set -- a setting that includes moment inequality problems and certain tests of shape restrictions as special cases." @default.
• W2952004221 created "2019-06-27" @default.
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• W2952004221 date "2014-04-14" @default.
• W2952004221 modified "2023-10-16" @default.
• W2952004221 title "Inference on Directionally Differentiable Functions" @default.
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• W2952004221 doi "https://doi.org/10.48550/arxiv.1404.3763" @default.
• W2952004221 hasPublicationYear "2014" @default.
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