Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inference on Directionally Differentiable Functions   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.

37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int