LARGE SAMPLE THEORY FOR MERGED DATA FROM MULTIPLE SOURCES

• 成果类型: Article
• 署名作者: Saegusa, Takumi
• 署名单位: University System of Maryland; University of Maryland College Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1727
• 发表日期: 2019
• 页码: 1585-1615
• 关键词: 2-phase stratified samples; central limit-theorems; Semiparametric models; weighted likelihood; invariance-principle; efficient estimation; regression-analysis; wilms-tumor; frame; DESIGN

摘要

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.