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Title: Empirical process for merged data from multiple overlapping sources Authors:  Takumi Saegusa - University of Maryland (United States) [presenting]
Abstract: Empirical process theory is studied for merged data from multiple overlapping data sources. The setting we consider is characterized by (1) heterogeneity of multiple data sets, (2) unidentified duplication across samples, (3) dependence due to finite population sampling. The resultant sample is a biased and dependent sample with duplication. The standard empirical process theory often assumes an independent and identically distributed sample, and hence most results do not hold in this setting. We develop the uniform law of large numbers and uniform central limit theorem for data integration. We apply these empirical process results to general theorems for consistency, rates of convergence and asymptotic normality of infinite dimensional M-estimators. The results are illustrated with simulation studies and a real data example using the Cox proportional hazards model.