Jackknifing Some Classes of Estimators in Survey Sampling

Abstract

Whenever some suitable auxiliary information is available on supplementary variate highly correlated with the study variate, it is the usual in practice in sample survey to utilize this information in the method of estimation to increase efficiency. A class of ratio-product estimators is suggested to estimate the population mean for the variable of interest using two auxiliary vatiables by applying .the jackknife technique of Quenouille (I 956), Durbin (I959) and furiher developed by Schucany et. aI. (I 971) to reduce the bias. Under simple random sampling with replacement (SRSWR), the mean square en-or (MSE) of the proposed estimator is obtained. The conditions for the proposed estimator to be more efficient than the conventional estimator(y), usual regression estimator for two auxiliary variable, Srivastava (I965), Singh (I967) and Abu-Dayyeh et. al. (2003) ratio cum product estimators are derived. An empirical study is can-ied out to demonstrate the efficiency of the proposed estimator is more than the other considered estimators. In addition, an unbiased technique is applied and observe that estimator is almost unbiased. Fmiher this technique is also used to obtain the minimum MSE of jackknife estimators under probability proportional to size with replacement (PPSWR) sampling technique. It turns out that estimator under PPSWR dominate oyer simple random sample (SRS) estimator y to estimate the population mean.