Estimator of Domain Mean Using Stratified Sampling in the Presence on Non-Response

Abstract

The present work investigated a direct estimator of domain mean which helps for future work in the field of small area estimation. Our investigation will helpful when the availability of non-response in strata which may or may not be the same in all the domains. We discussed the proposed estimators for domain mean utilizing stratified sampling with non-response and also studied its properties. Proposed estimator has compared with a direct ratio estimator for domain mean utilizing stratified sampling with non-response where, non-response is available approximately (30%) in the domain. We considered two situations in the first, non-responses are approximately (30%). However, in second case, different non-responses like 20 % and 40 % in the strata 1 and 2 respectively. An empirical study has been carried out for the data Sarndal et al. (1992) in terms of the mean square error. We obtained that proposed generalized investigation is more efficient than ratio estimator in case i over case ii. It is analyzed that the direct generalized investigation is a better choice over direct ratio estimate with or without non-responses in both the cases.

An Improved Product Estimator for Finite Population Mean in the Presence of Nonignorable Nonresponse

“…This suggests that the proposed estimator with lower biases provide more accurate estimates than the estimator by Ashutosh [1]. Regarding MSE values, the estimator by Ashutosh [1] generally presents lower MSES compared to the proposed estimator ( RDG,2,i) as reduced MSE further supports enhanced accuracy.…”

“…An increase in bias may indicate a deviation from the true values, while a decrease may imply improved accuracy. Implying the proposed estimator with less biases will present accurate estimates than the estimator by Ashutosh [1] . For the mean squared errors, the estimator by Ashutosh [1] generally present lower MSE values compared to the proposed estimator ( RDG,2,i).…”

“…Table 12 displays the bias and the mean squared errors of the proposed estimator (α = 2) based on subpopulations. In Table 12, it is evident that the proposed estimator ( RDG,2,i) exhibit lower biases across all subpopulations compared to the estimator by Ashutosh [1]. An increase in bias may signal a deviation from true values, while a decrease may imply improved accuracy.…”

“…The Tikkwal and Ghiya [15] estimator used a non-linear function of the auxiliary variable in their estimation process, thus allowing for a more flexible relationship between the auxiliary variable and the study variable. Ashutosh [1] revealed that in situation where nonignorable nonresponse is present, the Tikkwal and Ghiya [15] estimator performed better than other competing estimators. But the estimator of Ashutosh [1] is unable to overcome the assumption of linearity and hence, will be challenged when the relationship between the study and auxiliary variable.…”

“…Ashutosh [1] revealed that in situation where nonignorable nonresponse is present, the Tikkwal and Ghiya [15] estimator performed better than other competing estimators. But the estimator of Ashutosh [1] is unable to overcome the assumption of linearity and hence, will be challenged when the relationship between the study and auxiliary variable. Furthermore, literature acknowledged heterogeneous population confronted by sample surveyors introduces bias in the estimation of population parameters [16,17].…”