Journal of Statistical Theory and Applications (JSTA) (Mar 2020)
On a Class of Almost Unbiased Ratio Type Estimators
Abstract
In sample surveys ratio estimator has found extensive applications to obtain more precise estimators of the population ratio, population mean, and population total of the study variable in the presence of auxiliary information, when the study variable is positively correlated with the auxiliary variable. The theory underlying the ratio method of estimation is same whether we estimate the population ratio or population mean/population total, excepting the fact that in the latter case we assume the advance knowledge of the population mean or total of the auxiliary variable in question. In this paper we use the term ratio estimator for both the purposes. However, in spite of its simplicity the ratio estimator is accompanied by an unwelcome bias, although the bias decreases with increase in sample size and is negligible for large sample sizes. In small samples the bias may be substantial so as to downgrade its utility by affecting the reliability of the estimate. As pointed out by L.A. Goodman, H.O. Hartley, J. Am. Stat. Assoc. 53 (1958), 491–508, in sample surveys where we draw very small samples from a large number of strata in stratified random sampling with the ratio method of estimation in each stratum, the combined bias from all the strata may assume serious proportions, affecting the reliability of the estimate. This calls for devising techniques either at estimation stage or in the sampling scheme at the selection stage to reduce the bias or completely eliminating it to make it usable in practice. This has motivated many research workers like E.M.L. Beale, Ind. Organ. 31 (1962), 27–28 and M. Tin, J. Am. Stat. Assoc. 60 (1965), 294–307 among others to construct estimators at the estimation stage removing the bias of O(1/n), where n is the sample size, and thus reducing the bias to O(1/n2). Such estimators are termed as Almost Unbiased ratio-type estimators found in literature. In this paper we have proposed a class of almost ratio type estimators following the techniques of E.M.L. Beale, Ind. Organ. 31 (1962), 27–28 and M. Tin, J. Am. Stat. Assoc. 60 (1965), 294–307 and made comparison with regard to bias and efficiency.
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