Estimation of Population Mean in Two Stage Design using Double Sampling for Stratification and Multiauxiliary Information

Abstract

ABSTRACT For estimating the population mean of the heterogeneous population, when sampling frame in strata and the strata weight are not defined, we have proposed new difference and ratio estimators using double sampling for stratification and auxiliary information in two stage design. The expression for bias and variances of the proposed estimators have been obtained based on double sampling for stratification approach and comparison have been made with estimator under unstratified double sampling. In addition, we support these theoretical results by an empirical study . General Terms Sampling Theory � Keywords Double Sampling for Stratification; Two Stage Design; Auxiliary Information; Difference (D) and Ratio (R) estimators. 1. INTRODUCTION Information on variables correlated with the main variable under study is popularly known as auxiliary information which may be fruitfully utilized either at planning stage or at designing stage or at the estimation stage to arrive at improved estimator compared to those, not utilizing auxiliary information. If the required information is not available in advance for the entire population, it might be advantageous to collect certain items for large preliminary sample and then use this information at the estimation stage to improve the estimators. This technique is generally referred to as double sampling. Stratification is one of the most widely used techniques in sample survey design serving the dual purpose of providing samples that are representative of major sub-groups of the population and improving the precision of estimators. Stratified sampling presupposes the knowledge of strata size as well as the availability of a frame for drawing a sample in each stratum. However application of this technique presupposes the knowledge of strata size and the availability of sampling frames within strata. But in many practical situations, when we want to estimate the population mean 𝒀 of a variate y and consider it desirable to stratify the population, consisting of N units on the basis of the value of auxiliary character x but the information of x is unknown, the sampling frame for various strata and the strata weight 𝑾