Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic expansion of the minimum covariance determinant estimators   In arXiv:0907.0079 by Cator and Lopuhaa, an asymptotic expansion for the MCD
estimators is established in a very general framework. This expansion requires
the existence and non-singularity of the derivative in a first-order Taylor
expansion. In this paper, we prove the existence of this derivative for
multivariate distributions that have a density and provide an explicit
expression. Moreover, under suitable symmetry conditions on the density, we
show that this derivative is non-singular. These symmetry conditions include
the elliptically contoured multivariate location-scatter model, in which case
we show that the minimum covariance determinant (MCD) estimators of
multivariate location and covariance are asymptotically equivalent to a sum of
independent identically distributed vector and matrix valued random elements,
respectively. This provides a proof of asymptotic normality and a precise
description of the limiting covariance structure for the MCD estimators.

18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph