DEVELOPMENT OF ALMOST UNBIASED RATIO TYPE ESTIMATOR USING THE STANDARD DEVIATION WHEN AUXILIARY VARIABLE IS UNKNOWN

Abstract

Some authors had proposed modified ratio estimators of population mean using the population
parameter of the auxiliary when the information on the auxiliary is known. These estimators
are biased though with smaller mean square error compared to the classical ratio estimator.
However, the information on the auxiliary variable may not be available in all cases. In this
paper, the use of double sampling strategy was employed to obtain more information on the
auxiliary variable and then the almost unbiased ratio estimator of population mean using
standard deviation
x S
ˆ
is proposed. The mean square error and bias of the developed estimator
were derived, as well as the condition under which the developed estimator performs better
than the classical ratio estimator. To validate the merits of the proposed estimator over other
estimators, an empirical study carried out revealed that the proposed estimator has the smallest
bias among the existing estimators considered (0.0645 and 0.0175) for population 1 and
population 2 respectively. Similarly, with respect to mean square errors, the proposed
estimator has the least among the existing estimators considered (1.076 and 15.6953) for
population 1 and population 2 respectively.