Abstract
In the present study, we propose the proficient class of estimators of the finite population mean, while incorporating the nonconventional location and nonconventional measures of dispersion with coefficient of variation of the auxiliary variable. Properties associated with the suggested class of improved estimators are derived, and an efficiency comparison with the usual unbiased ratio estimator and other existing estimators under consideration in the present study is established. An empirical study has also been provided to validate the theoretical results. Finally, it is established that the proposed class of estimators of the finite population variance proves to be more efficient than the existing estimators mentioned in this study.
Highlights
It is very quite often that utilization of supplementary information in survey sampling which has some sort of strong positive or negative correlation with the response variable is always found to be advantageous
In the present study, we made the utilization of nonconventional location parameters, nonconventional measures of dispersion, and their functions with the coefficient of variation of the auxiliary variable in order to suggest the class of estimators for estimating the population variance. e properties of the proposed class of estimators are studied under large sample approximation
Consider a finite population Z (Z1, Z2, . . . , ZM) of M units and let (z, r) be the study and auxiliary variables defined on Z taking values, respectively, on Zi(i 1, 2, . . . , M)
Summary
It is very quite often that utilization of supplementary information in survey sampling which has some sort of strong positive or negative correlation with the response variable is always found to be advantageous. In case of extreme values, using classical methods of estimation provides misleading results, but authors have put their valuable efforts to come up with solutions to this situation, so that precise results should be obtained even with the presence of outliers in the data. Authors such as Subzar et al [13] have proposed different robust ratio type estimators in simple random sampling without replacement (SRSWOR) while utilizing the Huber-M estimation technique. It has been shown theoretically as well as empirically that the proposed class of estimators is more efficient than existing estimators mentioned in this study
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