A note on some nonresponse-adjusted estimator for the finite population coefficient of variation under double sampling

Issue title: Statistical Inference with Missing Data

Guest editors: Ma del Mar Rueda

Article type: Research Article

Authors: Gamrot, Wojciech

Affiliations: Department of Statistics, University of Economics, 1 Maja 50, 40-287 Katowice, Poland. Tel.: +48322577486; E-mail: gamrot@ae.katowice.pl

Abstract: In many situations the survey objectives are not limited to the estimation of simple population parameters like means or totals and include more complex characteristics. In particular it may be desirable to assess the population coefficient of variation. Various estimators of this parameter are discussed in the literature. Survey nonresponse may affect their properties by increasing the bias and/or variance. In this paper a nonresponse-corrected estimator of the population coefficient of variation based on double sampling for nonresponse is proposed. Its properties are studied for arbitrary sampling designs in both phases and the stochastic nonresponse model. An important special case of simple random sampling without replacement and deterministic nonresponse is also discussed. Then a more general situation of second phase nonresponse is considered and a comparison with the non-adjusted estimator is made.

Keywords: Coefficient of variation, nonresponse adjustment, double sampling

DOI: 10.3233/MAS-2008-3207

Journal: Model Assisted Statistics and Applications, vol. 3, no. 2, pp. 139-152, 2008