Efficient Estimation of Population Mean Using Incomplete Survey Data on Study and Auxiliary Characteristics

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 from 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.