Adjusted Confidence Bands for Complex Survey Data

Confidence bands in nonparametric regression have been studied for a long time with data assumed to be generated from independent and identically distributed (iid) random variables. The methods and theoretical results for iid data, however, do not directly apply to data from stratified multistage samples. In this paper, we extend the confidence bands introduced by Zhang and Lu (2008) for iid case to complex surveys based on an entirely data-driven procedure; the proposed confidence bands incorporate both the sampling weights and the kernel weights. Simulation studies show that the proposed method works well.