Restructured searls family of estimators of population mean in the presence of nonresponse

Abstract

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Nonresponse is a major problem encountered by surveyors when conducting sampling surveys. The present study suggested a naïve modified Searls method for the elevated estimation of the population mean of the primary variable under investigation by utilizing the known auxiliary parameters. The bias along with the mean squared error (MSE) of the introduced estimator is calculated up to the approximation of the first order. We compared the presented estimator with a competing usual unbiased estimator and other competing population mean estimators regarding the issue of nonresponse. The efficiency criteria of the introduced estimator outperforming the other estimators in the competition are determined and verified using five real data sets. The MSEs for the introduced estimator and the other estimators in the competition are calculated for the five considered populations. The estimator with the least MSE or highest percentage relative efficiency (PRE) is recommended for practical exercise in different areas of applications.

Keywords

• primary variable
• auxiliary variable
• non-response
• bias
• MSE
• PRE