An efficient estimator using median ranked set sampling for the finite population mean in case of nonresponse

Abstract

The classical estimator for the estimation of the finite population mean in the presence of nonresponse is the Hansen-Hurwitz estimator. This study first examines the use of ranked set sampling in the Hansen-Hurwitz estimator for both response and non-response groups. Subsequently, a new estimator
is proposed by employing median ranked set sampling for the same estimator. The sample selection is performed using the median ranked set sampling method for both response and non-response groups. A simulation study is conducted to investigate the efficiency of the estimators under different distributions, sample sizes, and subsample proportions, considering cases with perfect ranking and imperfect ranking. The obtained results are compared with various estimators available in the literature. Under unimodal symmetric distributions such as, Laplace and Normal distributions, the estimator based on the median ranked set sampling yields more efficient results, whereas under Uniform and Exponential distributions, the estimator based on the ranked set sampling is found to be more efficient. Moreover, the efficiency of the proposed estimator has been evaluated using real-life data. The proposed estimator has been found to produce more efficient results compared to other estimators in the presence of non-response.