Estimation of the Population Variance Using a Smoothing Operator Under Simple Random Sampling

Abstract

Variance estimation has been a major concern in sample survey theory. The problem in estimation theory is to determine estimators that have smaller variance under a given model speci cation. However, existing variance estimators su er from boundary problems and outlier sensitivity. To address this, a robust variance estimate of the ratio estimator of the population mean using a multiplicative bias correction technique under model based approach is considered. Asymptotic properties of the robust variance estimator are investigated. Also a comparative study of the existing variance estimators and the derived robust variance estimator of the population mean is studied. The results of the study show that under mild assumption, the derived variance estimator of the population mean is asymptotically more consistent and has a better coverage probability as compared to rival variance estimators of the population mean.