A new class of robust ratio estimators for finite population variance

Abstract

It is a general practice to use robust estimates to improve ratio estimators using functions of the parameters of an auxiliary variable. In this study, a new class of robust estimators based upon the minimum covariance determinant (MCD) and the minimum volume ellipsoid (MVE) robust covariance estimates have been suggested for estimating population variance in the presence of outlier values in the data set for the simple random sampling. The expression for the mean square error (MSE) of the proposed class of estimators is derived from the first degree of approximation. The efficiency of the proposed class of robust estimators is compared with some competing estimators discussed in the literature, and found that proposed estimators are better than other mentioned estimators here. In addition, real data set and simulation studies are performed to present the efficiencies of the estimators. We demonstrate theoretically and numerically that the proposed class of estimators performs better than all other competitor estimators under all situations.

Calibration Approach for Variance Estimation of Small Domain

“…Särndal et al [20] provided the variance of the GREG estimator. Zaman and Bulut [21] recently discussed the variance of ratio estimators. e proposed estimator is like a regression estimator.…”

Improved Estimation of Finite Population Variance Using Dual Supplementary Information under Stratified Random Sampling

“…Isaki [2] discussed the variance estimation using ratio and regression-type estimators. Some important references regarding variance estimation include Garcia and Cebrian [3]; Arcos et al [4]; Shabbir and Gupta [5]; Singh and Solanki [6]; Adichwal et al [7,8], Ahmad et al [9]; Shabbir and Gupta [10]; Singh and Khalid [11,12] and Zaman and Bulut [13].…”

A simulation study: Improved ratio-in-regression type variance estimator based on dual use of auxiliary variable under simple random sampling

“…For proper treatment, a doctor must have a detailed realization of differences in human hypertension and fever. Many authors suggested different types of estimators for variance including Das [1], Prasad and Singh [2], Swain and Mishra [3], Ahmad and Shabbir [4], Kadilar and Cingi [5], Subramani and Kumarapandiyan [6], Singh and Solanki [7], Yadav et al [8], Singh et al [9], Yadav and Kadilar [10], Adichwal et al [11,12], Yasmeen et al [13], Zaman [14,15], Zaman and Bulut [16], Zaman et al [17,18], Bhushan et al [19], Shahzad et al [20], Ahmad et al [21], Ozturk [22], Ozturk and Demirel [23], Frey and Feeman [24], Zamanzade and Vock [25], Mahdizadeh and Zamanzade [26,27], Bhushan et al [28], Bhushan et al [29], Zaman and Bulut [30,31], Yadav and Zaman [32], Zaman and Kadilar [33], Zaman and Dunder [34] and Singh and Khalid [35]. We requisite to estimate population parameters for numerous variables in multidisciplinary surveys, such as house lengths, income level, and the number of unemployed people, in socio-economic surveys.…”