Generalized Variance Estimator using Auxiliary Information in the Presence and Absence of Measurement Error

Abstract

In this study, we have proposed a new generalized estimator using auxiliary information for the estimation of population variance in presence and absence of measurement error. The expressions approximate bias and mean square error of the proposed generalized estimator are derive up to the first-order. Several new and existing estimators are found as the special cases of proposed estimator and expressed on various values of optimizing and generalized constants. The proposed estimator is compared mathematically with some existing estimators under certain conditions. The performance of proposed estimator is observed by simulation and real data application under different sample sizes. It is observed that the proposed estimator performed well than other competing estimators in the presence and absence of measurement error.

Modified correlated measurement errors model for estimation of population mean utilizing auxiliary information

“…Without taking the MEs into consideration, the estimates seem incomplete which misleads the inference of the study. Various authors including Shalabh 7 , Manisha and Singh 8 , Singh and Karpe 9 – 13 , Diana and Giordan 14 , Gupta et al 15 , Tariq et al 16 , 17 and Singh et al 18 have focused on the estimation of various parameters such as population mean, total, ratio, product and variance under MEs.…”

“…Thus, the resulting modified correlated MEs model is:with |α| < 1 and |η| < 1.Here we note that α and η may take the values of ρ YX and ρ uv as |ρ YX | < 1 and |ρ uv | < 1. Now we define the ratio ( t * R ) and product ( t * P ) estimators for population mean µ Y of Y under the model(17) asTo study the properties of the estimators t…”

Efficient imputation methods in case of measurement errors

“… [6] discussed the estimation of population variance under MEs. [7] and [8] suggested some population variance estimation methods utilizing supplementary data in the absence and presence of MEs. [9] , [10] , [11] evaluated the performance of several classes of estimators under the impact of the correlated MEs.…”

Impact of Correlated Measurement Errors on Some Efficient Classes of Estimators

“…Hussain et al [9] suggested the estimation of a fnite population distribution function with the dual use of supplementary information under nonresponse. Tariq et al [10] proposed a supplementary information-based variance estimator to tackle the problem of ME. Tariq et al [11] suggested a generalized variance estimator utilizing supplementary information in the presence and absence of ME.…”

“…Tariq et al [10] proposed a supplementary information-based variance estimator to tackle the problem of ME. Tariq et al [11] suggested a generalized variance estimator utilizing supplementary information in the presence and absence of ME. Zahid et al [12] developed a generalized class of estimators for the sensitive variables in the case of ME and nonresponse.…”