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

Jianqiang C. Wang

Computational Statistics & Data Analysis, 2012, vol. 56, issue 3, 664-679

Abstract: 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.

Keywords: Anderson–Darling test; Convergence in functional space; Kolmogorov–Smirnov test; Gaussian process; Rao–Kovar–Mantel estimator (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947311003343
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:3:p:664-679

DOI: 10.1016/j.csda.2011.09.015

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().