Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Fiducial Inference for Ultrahigh Dimensional Regression   In recent years the ultrahigh dimensional linear regression problem has
attracted enormous attentions from the research community. Under the sparsity
assumption most of the published work is devoted to the selection and
estimation of the significant predictor variables. This paper studies a
different but fundamentally important aspect of this problem: uncertainty
quantification for parameter estimates and model choices. To be more specific,
this paper proposes methods for deriving a probability density function on the
set of all possible models, and also for constructing confidence intervals for
the corresponding parameters. These proposed methods are developed using the
generalized fiducial methodology, which is a variant of Fisher's controversial
fiducial idea. Theoretical properties of the proposed methods are studied, and
in particular it is shown that statistical inference based on the proposed
methods will have exact asymptotic frequentist property. In terms of empirical
performances, the proposed methods are tested by simulation experiments and an
application to a real data set. Lastly this work can also be seen as an
interesting and successful application of Fisher's fiducial idea to an
important and contemporary problem. To the best of the authors' knowledge, this
is the first time that the fiducial idea is being applied to a so-called "large
p small n" problem.

15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
2
The categories of this paper are: math