© 2010 Pakistan Journal of Statistics 203 Pak. J. Statist. 2009 Vol. 26(1), 203-238 A GENERAL CLASS OF DSS ESTIMATORS OF POPULATION RATIO, PRODUCT AND MEAN IN THE PRESENCE OF NON-RESPONSE BASED ON THE SUB-SAMPLING OF THE NON-RESPONDENTS Housila P. Singh 1 and Sunil Kumar 2 School of Studies in Statistics, Vikram University, Ujjain-456010, M.P., India Email: 1 hpsujn@rediffmail.com 2 sunilbhougal06@gmail.com ABSTRACT The paper deals with the problem of estimating the general parameter ( ) P  {   0 1 , Y Y   1 0, Y   being a scalar which takes values -1, 0 and 1; and j Y is the population mean of the study variate , 0,1 j y j  } using double sampling for stratification (DSS) based on auxiliary information (i) when there is total response on the auxiliary variable x used in estimating the stratum weight h W {   , h h N N N  and N being the size of the th h stratum and the population size N respectively} and on the study variates   0 1 , y y ; and (ii) when there is total response on the auxiliary variable x and incomplete response on the study variables   0 1 , y y , see Okafor (1996). Classes of estimators for the general parameter ( ) P  in both the situations have been proposed and their properties are studied. Asymptotic optimum estimators (AOEs) in the classes are investigated alongwith their approximate variance formulae. The present study also generalizes the work of Okafor (1996) and Singh and Vishwakarma (2007). KEY WORDS Auxiliary variate; Study variates; Double sampling for stratification; Non-response; Sub-sampling. 1. INTRODUCTION A stratified sampling design, in which a finite population is divided into non- overlapping strata and samples are drawn from each stratum, is a common and effective procedure for reducing sampling error. It is also well known that the use of auxiliary information in stratifying the population improve the precision of an estimate. In some practical situations the information on the auxiliary variable required for stratification of units, e.g. age, sex, household size, etc. is not available. In such a situation we use the technique of double sampling for stratification (DSS) in which the information required for stratification is gathered at the first phase of sampling. Rao (1973) suggested a technique of double sampling for stratification (DSS) which consists of the following steps: