Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean Shrinkage Estimation for High-Dimensional Diagonal Natural
  Exponential Families   Shrinkage estimators have been studied widely in statistics and have profound
impact in many applications. In this paper, we study simultaneous estimation of
the mean parameters of random observations from a diagonal multivariate natural
exponential family. More broadly, we study distributions for which the diagonal
entries of the covariance matrix are certain quadratic functions of the mean
parameter. We propose two classes of semi-parametric shrinkage estimators for
the mean vector and construct unbiased estimators of the corresponding risk.
Further, we establish the asymptotic consistency and convergence rates for
these shrinkage estimators under squared error loss as both $n$, the sample
size, and $p$, the dimension, tend to infinity. Finally, we consider the
diagonal multivariate natural exponential families, which have been classified
as consisting of the normal, Poisson, gamma, multinomial, negative multinomial,
and hybrid classes of distributions. We deduce consistency of our estimators in
the case of the normal, gamma, and negative multinomial distributions if $p
n^{-1/3}\log^{4/3}{n} \rightarrow 0$ as $n,p \rightarrow \infty$, and for
Poisson and multinomial distributions if $pn^{-1/2} \rightarrow 0$ as $n,p
\rightarrow \infty$.

24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ