No abstract

The efficiencies of the ratio-type estimators have been increased by using linear transformation on auxiliary variable in the literature. But such type of estimators requires the additional knowledge of unknown population parameters, which restricts their applicability. Keeping in view such restrictions, we have proposed two unbiased estimators of population mean of study variable on applying linear transformation to auxiliary variable by using its extreme values in the population that are generally available in practice. The comparison of the proposed estimators with the existing ones have been done with respect to their variances. It has also been shown that the proposed estimators have greater applicability and are more efficient than the mean per unit estimator even when the existing estimators are less efficient. We have also shown that under some known conditions the choice of most efficient estimators among the considered ones can be made for a given population. The theoretical results obtained are shown diagrammatically and have been verified numerically by taking some empirical populations.

For estimating the mean of a finite population, Srivastava and Jhajj (1981) defined a broad class of estimators which we information of the sample mean as well as the sample variance of an auxiliary variable. In this paper we extend this class of estimators to the case when such information on p(> 1) auxiliary variables is available. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters. When these population parameters are replaced by their consistent estimates, the resulting estimators are shown to have the same asymptotic mean squared error. An expression by which the mean squared error of such estimators is smaller than those which use only the population means of the auxiliary variables, is obtained.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYFor estimating the mean of a finite population using information on an auxiliary variable, a class of estimators is defined as a function of the ratio of sample mean to population mean and the ratio of sample variance to population variance of the auxiliary variable. Asymptotic expressions for bias and mean squared error are obtained. A condition is given for the minimum mean squared error of estimators of this class to be smaller than those which use only the ratio of sample mean to population mean of the auxiliary variable.

No abstract