Enhancing the efficiency of the ratio-type estimators of population variance with a blend of information on robust location measures

Abstract

Numerous ratio-type estimators of the population variance are proposed in the existing literature based on different characteristics of the study as well as the auxiliary variable. However, mostly the existing estimators are based on the conventional measures of the population characteristics and their efficiency is dubious in the presence of outliers in the data. This study presents improved families of variance estimators under simple random sampling without replacement assuming that the information on some robust nonconventional location parameters of the auxiliary variable is known besides the usual conventional parameters. The bias and mean square error of the proposed families of estimators are obtained and the efficiency conditions are derived mathematically. The theoretical results are supplemented with the numerical illustrations by using real datasets which indicates the supremacy of the suggested families of estimators.

A new improved class of ratio-product type exponential estimators of the population variance

“…Taking motivation from Shabbir and Gupta [17] and Naz, Abid, Nawaz and Pang [34] we have integrated the above mentioned non-conventional robust measures of dispersion to design a stable ratio product type exponential estimator of population variance defined as. : For Simplification, expanding Eqn.…”

“…The use of these estimators is expanding to a variety of fields such as yield estimation in agriculture, demographic studies, environmental Recently, ratio-type estimators for estimation of population mean have been developed which incorporate auxiliary information on nonconventional measures [28][29][30][31][32]. These non-conventional measures are somewhat robust and outlier resistant which aids in stabilizing the mean square error of the estimators in presence of outliers [8,33,34]. Use of auxiliary information on non-conventional or robust measures for estimation of population variance is still a neglected area.…”

An Improved and Robust Class of Variance Estimator

“…A major disadvantage related with the estimators proposed by Isaki [3], Upadhyaya and Singh [4], Kadilar and Cingi [5], Subramani and Kumarapandiyan [6][7][8][9] and Khan and Shabbir [10] is that these estimators lose their efficiency and performance ability in the presence of outliers (cf. Abid et al [25][26] and Naz et al [27]). In case of outliers, robust estimators are preferred and are of more practical use, because these estimators are not affected by the outliers.…”

Quantile regression-ratio-type estimators for mean estimation under complete and partial auxiliary information

“…[11], Hanif and Shahzad [12] have developed some classes of estimators utilizing 2 supplementary information under simple random sampling scheme. However, for positive correlation, traditional regression-ratio-type estimator is better for the estimation of population parameters (see, e.g., Abid et al [13]; Irfan et al [14]; Naz et al [15], Abid et al [16]). Note that traditional regression-typeratio estimators based on conventional regression coefficient i.e.…”