A general class of estimators with auxiliary information based on available units M.M. Rueda a, * , S. Gonza ´lez b , A. Arcos a a Department of Statistics & OR, Facultad de Ciencias, Avda. Fuentenueva, University of Granada, 18071, Granada, Spain b Department of Statistics & OR, University of Jae ´n, 23071, Jae ´n, Spain Abstract This paper proposes some estimators for the finite population mean when observa- tions on some units (on either the auxiliary variable or the main variable) are missing. The optimum estimator in the proposed class is derived. Asymptotic properties of opti- mum estimator are studied. A brief simulation study shows goods properties for mod- erate sample sizes. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Auxiliary information; Missing data 1. Introduction Surveys often suffer from the problem of nonresponse. In a survey study, data may be missing due to a variety of reasons; the respondent may not be 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.07.018 * Corresponding author. E-mail address: mrueda@ugr.es (M.M. Rueda). Applied Mathematics and Computation 175 (2006) 131–148 www.elsevier.com/locate/amc