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. (C) 2011 Elsevier B.V. All rights reserved.