Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large Sample Theory for Merged Data from Multiple Sources   We develop large sample theory for merged data from multiple sources. Main
statistical issues treated in this paper are (1) the same unit potentially
appears in multiple datasets from overlapping data sources, (2) duplicated
items are not identified, and (3) a sample from the same data source is
dependent due to sampling without replacement. We propose and study a new
weighted empirical process and extend empirical process theory to a dependent
and biased sample with duplication. Specifically, we establish the uniform law
of large numbers and uniform central limit theorem over a class of functions
along with several empirical process results under conditions identical to
those in the i.i.d. setting. As applications, we study infinite-dimensional
M-estimation and develop its consistency, rates of convergence, and asymptotic
normality. Our theoretical results are illustrated with simulation studies and
a real data example.

28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org