Robustness of estimator of the finite population total developed by Singh et al. (2018) under specified error-invariables super population model (0, 1: 1) and (0, 1: x) has been investigated if these model deviate. Measurement error in the study variate y is only considered. It has been found that under balanced sample [Royall and Herson (1973a)], the percent loss in precision is quite small up
... [Show full abstract] to about 7% under the model (0, 1: x) with balanced sampling. The results also indicate that it is important to ascertain in advance the variance structure V(x) in auxiliary variable x related to study variate y when the model is specified for the development of estimator.