The Annals of Statistics
- Ann. Statist.
- Volume 47, Number 3 (2019), 1585-1615.
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.
Ann. Statist., Volume 47, Number 3 (2019), 1585-1615.
Received: February 2017
Revised: May 2018
First available in Project Euclid: 13 February 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Saegusa, Takumi. Large sample theory for merged data from multiple sources. Ann. Statist. 47 (2019), no. 3, 1585--1615. doi:10.1214/18-AOS1727. https://projecteuclid.org/euclid.aos/1550026850
- Supplement to “Large sample theory for merged data from multiple sources.”. The proofs and additional simulations are given in the Supplement .