Sample distribution function based goodness-of-fit test for complex surveys

Testing the parametric distribution of a random variable is a fundamental problem in exploratory and inferential statistics. Classical empirical distribution function based goodness-of-fit tests typically require the data to be an independent and identically distributed realization of a certain probability model, and thus would fail when complex sampling designs introduce dependency and selection bias to the realized sample. In this paper, we propose goodness-of-fit procedures for a survey variable. To this end, we introduce several divergence measures between the design weighted estimator of distribution function and the hypothesized distribution, and propose goodness-of-fit tests based on these divergence measures. The test procedures are substantiated by theoretical results on the convergence of the estimated distribution function to the superpopulation distribution function on a metric space. We also provide computational details on how to calculate test p-values, and demonstrate the performance of the proposed test through simulation experiments. Finally, we illustrate the utility of the proposed test through the analysis of US 2004 presidential election data.