Hindawi Publishing Corporation Journal of Probability and Statistics Volume 2012, Article ID 214959, 12 pages doi:10.1155/2012/214959 Research Article Double Sampling with Ranked Set Selection in the Second Phase with Nonresponse: Analytical Results and Monte Carlo Experiences Gaajendra K. Agarwal, 1 Sira M. Allende, 2 and Carlos N. Bouza 2 1 Software Development Division, Institute of Computing Training, Cuba 2 Universidad de La Habana, Habana, Cuba Correspondence should be addressed to Carlos N. Bouza, bouza@matcom.uh.cu Received 19 May 2011; Revised 5 December 2011; Accepted 21 December 2011 Academic Editor: Man Lai Tang Copyright q 2012 Gaajendra K. Agarwal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper is devoted to the study of the behavior of the use of double sampling for dealing with nonresponses, when ranked set sample is used. The characteristics of the sampling strategies are derived. The structure of the errors generated the need of studying of the optimality of the strategies by performing a set Monte Carlo experiments. 1. Introduction The usual theory of survey sampling is developed assuming that the finite population U  {u 1 ,...,u N } is composed by individuals that can be perfectly identified. A sample s of size n ≤ N is selected. The variable of interest Y is measured in each selected unit. Real-life surveys should deal the existence of missing observations. There are three solutions to cope with this fact: to ignore the nonrespondents, to subsample the nonrespondents, or to impute the missing values. To ignore the non responses is a dangerous decision, to sub sample is a conservative and costly solution. Imputation is often used to compensate for item nonre- sponse. See, for discussions on the theme, Rueda and Gonz ´ alez 1, Singh 2, for example. Section 2 presents the problem of non response when a single sample is selected. We consider the use of double sampling for obtaining information on an auxiliary vari- able X. A first large sample is selected, it is supposedly noncostly. The values of X are used for selecting a ranked set sample RSS, as the units are ranked using the values in the first stage sample. A selection of second sample provides a subsample from the preliminary large sample. The literature on the use of simple random double sampling SRS is large. Text books give the basic theory, see Singh 2 and Cochran 3. In this paper we consider a ranked set