Estimation of mean using double sampling the non-respondents with known and unknown variance (Q2224043)

Summary: The objective of this article is to suggest improved classes of estimators for estimating the population mean using known and unknown variance of study character under incomplete information to improve the efficiency of the usual unbiased estimator suggested by \textit{M. H. Hansen} and \textit{W. N. Hurwitz} [``The problem of non-response in sample surveys'', J. Am. Stat. Assoc. 41, No. 236, 517--529 (1946; \url{doi:10.1080/01621459.1946.10501894})]. The expressions for bias and mean square error of the proposed classes of estimators are obtained up to the terms of order \(n^{-2}\) under large sample approximation. Several sub-classes of estimators are introduced and their properties are studied. A comparative study of the suggested classes of estimators is carried out with an empirical study based on real dataset of census handbook published by Government of India.