Improved Ratio Estimators Using Some Robust Measures

Abstract

Estimation of population mean is of prime concern in many studies and ratio estimators are popular choices for it. It is a common practice to use conventional measures of location to develop ratio estimators using information on auxiliary variables. In this article, we propose a class of ratio estimators for a finite population mean using information on two auxiliary variables with the help of some non-conventional location measures. We have incorporated tri-mean, Hodges-Lehmann, mid-range and decile mean of the two auxiliary variables to serve the purpose. The properties associated with the proposed class of ratio estimators are evaluated using mean square error. We have presented efficiency comparisons of the proposed class of ratio estimators with other existing estimators under the optimal conditions. An empirical study is also included for illustration and verification purposes. From theoretical and empirical study, we observed that the proposed estimators perform better as compared to the usual ratio and the existing estimators consider in this study.

A new class of robust ratio estimators for finite population variance

“…The MSE of these estimators is given in (16). We obtained the MSE values of proposed classical estimators in (15), the unbiased estimator, Isaki estimator in (2), Singh et al estimator in (4), the regression estimator in (7), Upadhyaya and Singh estimator in (9), and Kadilar and Cingi estimators in (11). These values are given in the uncontaminated data part of Table 4.…”

“…Efficient estimators for the population variance has been discussed by various authors referred to Kadilar and Cingi [1], Khan and Shabbir [2], Singh et al [3], Yadav et al [4], Yaqub and Shabbir [5], Singh and Pal [6], Sanaullah et al [7], Muneer et al [8], Housila et al [9] and Sharma et al [10]. However, in the presence of unusual observations in the data, since the classical estimators are sensitive to these extreme values, their efficiencies decrease [11]. Therefore, to reduce the negative effect of the unusual observation problem in the data, it is suggested to use the robust regression estimate, the minimum covariance determinant (MCD), and the minimum volume ellipsoid (MVE) estimators instead of the classical ones.…”

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

“…Thus, these datasets are a good realization of the both with and without outlier observation cases. Moreover, these population datasets are frequently used in many studies to compare the performance of various estimators of population mean and variance, see for example, [28,29,33,48,49]…”

“…The ratio, product, regression, exponential and their different combinations are a popular choice, in practice, to enhance the efficiency of the estimators of population mean and variance in the presence of auxiliary information correlated with the study variable. 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].…”

On enhanced exponential‐cum‐ratio estimators using robust measures of location

“…28 Nowadays the estimators based on robust techniques got popularity in the literature of survey sampling. Abid et al 29 enhanced the performance of ratio estimators using some robust measures of location and dispersion. Zaman 30 and Zaman and Bulut 31 introduced improved and modified ratio estimators based on some robust regression methods.…”