Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical dimension in profile semiparametric estimation   This paper revisits the classical inference results for profile quasi maximum
likelihood estimators (profile MLE) in the semiparametric estimation problem.
We mainly focus on two prominent theorems: the Wilks phenomenon and Fisher
expansion for the profile MLE are stated in a new fashion allowing finite
samples and model misspecification. The method of study is also essentially
different from the usual analysis of the semiparametric problem based on the
notion of the hardest parametric submodel. Instead we derive finite sample
deviation bounds for the linear approximation error for the gradient of the
loglikelihood. This novel approach particularly allows to address the important
issue of the effective target and nuisance dimension. The obtained
nonasymptotic results are surprisingly sharp and yield the classical asymptotic
statements including the asymptotic normality and efficiency of the profile
MLE. The general results are specified to the important special cases of an
i.i.d. sample and the analysis is exemplified with a single index model.

17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin