Efficient estimation of population mean using incomplete survey data on study and auxiliary characteristics

Abstract

This paper considers the problem of estimating the population mean using the ratio and product methods when some observations in the sample data are missing at random and the population mean of the auxiliary characteristic is not known. Besides an unbiased estimator arising from the total discard of incomplete pairs of observations, four generally biased estimators are presented. The first two estimators arise form the partial utilization of data while the remaining two are based on full utilization. A comparative study of the efficiency properties of estimators is reported and the choice of estimators is discussed.