Title: Large Sample Theory for Multiple Frame Sampling

Abstract: Multiple-frame sampling is a commonly used sampling technique in sample surveys that takes multiple sam- ples from distinct but overlapping sampling frames. Main statistical issues are (1) the same unit can be sampled multiple times from different frames with different probabilities, and (2) a sample from each frame is dependent due to sampling without replacement. We study weighted empirical process based on Hartley's estimator, and extend empirical process theory to our non-i.i.d. setting without requiring additional design conditions. We apply our results to semiparametric inference.