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In real life, situations may arise when the available data are insufficient to provide accurate estimates for the domain, the small area estimation (SAE) technique has been used to get accurate estimates for the variable under study. The problem of missing data is a serious problem that has an impact on sample surveys, but small area estimates are especially prone to it. This paper is a basic effort that suggests design based synthetic imputation methods for the domain mean estimation using simple random sampling in order to address the issue of missing data under SAE. The expression of the mean square error for the proposed imputation methods are obtained up to first order approximation. The efficiency conditions are determined and a thorough simulation study is carried out using artificially generated data sets. An application is included with real data that further supports this study. [ABSTRACT FROM AUTHOR]

This article deals with some new imputation methods by extending the work of Bhushan and Pandey using multi-auxiliary information. The popularly used imputation like mean imputation, ratio method of imputation, regression method of imputation and power transformation method are special cases of the proposed methods apart from being less efficient than the proposed methods. The proposed imputation methods can be considered as an efficient extension to the work of Singh and Deo (Stat Pap 44:555–579, 2003), Singh (Stat A J Theor Appl Stat 43(5):499–511, 2009), Ahmed et al. (Stat Transit 7(6):1247–1264, 2006), Diana and Perri (Commun Stat Theory Methods 39:3245–3251, 2010) and Bhushan and Pandey (J Stat Manag Syst 19(6):755–769, 2016, Commun Stat Theory Methods 47(11):2576–2589, 2018). The theoretical results are derived and comparative study is conducted using real and simulated data and the results are found to be quite encouraging providing the improvement over the all discuss work. [ABSTRACT FROM AUTHOR]