A GENERALIZED CLASS RATIO-TYPE ESTIMATOR OF POPULATION MEAN BASED ON POST STRATIFICATION AND SUB-SAMPLING OF NON– RESPONDENTS

Abstract

Several authors have considered estimators aimed at reducing the bias due to nonresponse  in the estimation of the population mean, of a study variable y. Hansen and Hurwiz (1946) suggested a simple unbiased estimator y , in their attempt to reduce the nonresponse bias present in a survey. Similarly, Rao (1986) proposed an unbiased estimator y_ps  for practical situations that do frequently arise whereby one considers it desirable to make use of an auxiliary variable x (with full response) in post-stratifying the nonrespondents, even though its population mean X,  as well as the sampling frame within each stratum are both unknown, and the strata weight          W_{h(h=,….,L) obsolete.}  Sodipo (1998) developed the work of Rao (1986) by constructing a ratio-type estimator  g₁, which was shown to be more efficient. In this present study, we propose a class ratio-type estimator g₂, which is proved (theoretically and empirically) to be more efficient than, and also contains, the last two of the three existing estimators mentioned earlier. Expression for the optimum values of n and k_h(h=2…,L) are also derived, using a relevant cost function.