Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal robust estimators for families of distributions on the integers   Let F_{{\theta}} be a family of distributions with support on the set of
nonnegative integers Z_0. In this paper we derive the M-estimators with
smallest gross error sensitivity (GES). We start by defining the uniform median
of a distribution F with support on Z_0 (umed(F)) as the median of x+u, where x
and u are independent variables with distributions F and uniform in [-0.5,0.5]
respectively. Under some general conditions we prove that the estimator with
smallest GES satisfies umed(F_{n})=umed(F_{{\theta}}), where F_{n} is the
empirical distribution. The asymptotic distribution of these estimators is
found. This distribution is normal except when there is a positive integer k so
that F_{{\theta}}(k)=0.5. In this last case, the asymptotic distribution
behaves as normal at each side of 0, but with different variances. A simulation
Monte Carlo study compares, for the Poisson distribution, the efficiency and
robustness for finite sample sizes of this estimator with those of other robust
estimators.

32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th