Variance Estimators in the Presence of Measurement Errors Using Auxiliary Information
Keywords:Mean square error, measurement error, ratio-type estimators, percentage relative efficiency
Estimation of variance is very important in the area of sample survey. It provides the information on the accuracy of the estimators and allows drawing valid conclusion about the true value of the population parameter. Measurement error is a serious problem in survey sampling which arises when the answer provide by the respondents departs from the true value. This paper discussed the estimation problem of finite population variance using the information of the auxiliary variable in presence of measurement error under simple random sampling (SRS) design. Here some estimators for population variance have been suggested for the study variable Y. The proposed estimators based on arithmetic mean, harmonic mean and geometric mean of the sample variance estimator, ratio estimator and exponential ratio estimator. The approximate expressions of biases and mean square errors (MSEs) derived and calculated for the suggested estimators up to the first order using Taylor expansion. The efficiency comparisons of the suggested estimators have been made with the existing estimators. A numerical study also conducted to support the performance of suggested estimators.