© 2014 Pakistan Journal of Statistics 465 Pak. J. Statist. 2014 Vol. 30(4), 465-486 GENERALIZED ESTIMATOR FOR ESTIMATING POPULATION MEAN UNDER TWO STAGE SAMPLING Riffat Jabeen 1§ , Aamir Sanaullah 2 and Muhammad Hanif 3 National College of Business Administration and Economics, Lahore, Pakistan Email: 1 riffat.jabeen79@gmail.com 2 chaamirsanaullah@yahoo.com 3 drmianhanif@gmail.com § Corresponding author ABSTRACT Koyuncu and Kadilar (2009) proposed a family of ratio-type estimators for population mean using auxiliary information in simple random sampling. Srivastava and Garg (2009) proposed a general class of ratio estimator for estimating population mean using auxiliary variablein two-stage sampling. In this paper, motivated by Srivastava and Garg (2009) and Koyuncu and Kadilar (2009) we have proposed a general class of estimators for population mean for three different cases in two-stage sampling design. The mean square error (MSE) and bias expressions have been obtained in a general form up to the first order of approximation for the three cases. It has also been shown that for each of the three cases in two-stage sampling, minimum MSE of this class is asymptotical equal to the MSE of regression estimator. An empirical study has also been carried out, in order to demonstrate the performance of proposed general class of estimators for three cases in two-stage sampling design. KEYWORDS Auxiliary variable; mean square error; two stage sampling; first stage sampling unit; second stage sampling unit. 1. INTRODUCTION When nature of a population is to visualize in some clusters, a multi-stage sampling design is be more suitable. In sampling survey, it is often valuable if the units are sampled in more than one-stage [Cochran 1977, Kalton 1983, and Sarndal et al. 1992]. Morris (1955), and Leroux and Reimer (1959) discussed some applications of two-stage sampling design. Seelbinder (1951) discussed method to determine the first stage sampling units and the method for the selecting two-stage sampling units under without replacement taking probability of inclusion proportional to size, has been illustrated by Durbin (1967). Brewer and Hanif (1970) extended the work of Durbin (1967) to a general case. For rare and clustered populations Seber (1982) used two-stage sampling design in various situations. The idea was devised by Jensen (1994) independently. Whittemore (1997) provided the use of multi-stage sampling design and inference using maximum likelihood estimator (MLE) and Horvitz-Thompson (1952).