It is well-known that the appearance of measurement errors spoils the traditional results in survey sampling. The concept of correlated measurement errors (CMEs) is true in various practical situations, but this has been seldom considered by researchers in survey sampling. In this article, the influence of the CME under simple random sampling (SRS) has been considered over some prominent classes of estimators for the population mean. The first-order approximated formulae of the mean square error of the introduced estimators are reported, and a comparative analysis has also been conducted with traditional estimators. The theoretical findings are extended by a broad spectrum computational study using real and artificial data.

This manuscript develops few efficient difference and ratio kinds of imputations to handle the situation of missing observations given that these observations are polluted by the measurement errors (ME). The mean square errors of the developed imputations are studied to the primary degree approximation by adopting Taylor series expansion. The proposed imputations are equated with the latest existing imputations presented in the literature. The execution of the proposed imputations is assessed by utilizing a broad empirical study utilizing some real and hypothetically created populations. Appropriate remarks are made for sampling respondents regarding practical applications.