Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Density estimation for biased data   The concept of biased data is well known and its practical applications range
from social sciences and biology to economics and quality control.
  These observations arise when a sampling procedure chooses an observation
with probability that depends on the value of the observation. This is an
interesting sampling procedure because it favors some observations and neglects
others. It is known that biasing does not change rates of nonparametric density
estimation, but no results are available about sharp constants.
  This article presents asymptotic results on sharp minimax density estimation.
  In particular, a coefficient of difficulty is introduced that shows the
relationship between sample sizes of direct and biased samples that imply the
same accuracy of estimation. The notion of the restricted local minimax, where
a low-frequency part of the estimated density is known, is introduced; it sheds
new light on the phenomenon of nonparametric superefficiency.
  Results of a numerical study are presented.

19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ