Abstract
In the present paper, we have proposed some improved estimators of the population mean utilizing the information on two auxiliary variables adopting the idea of two-phase sampling under non-response. In order to propose the estimators, we have assumed that the study variable and first auxiliary variable suffer from non-response while the second (additional) auxiliary variable is free from non-response. We have derived the expressions for biases and mean square errors of the proposed estimators and compared them with that of usual estimator and some well known existing estimators of the population mean. The theoretical results have also been illustrated with some empirical data.
Highlights
IntroductionThe information on more than one auxiliary variable is available
In some practical situations, the information on more than one auxiliary variable is available
It is always seen that the responding units are not very similar to the non-responding units and the non-response plays an important role in such situations
Summary
The information on more than one auxiliary variable is available. Olkin(1958) was the first who proposed multivariate ratio estimator of the population mean utilizing the information on a number of auxiliary variables. The authors such as Cochran(1977), Olkin(1986), Khare and Srivastava(1993),Khare and Srivastava (1995), Okafor and Lee(2000), Tabasum and Khan(2004), Tabasum and Khan(2006), Singh and Kumar(2007), Singh and Kumar(2009),Chaudhary and Smarandache(2014), Pal and Singh (2018),Khare and Sinha(2019) have discussed the problem of non-response in two-phase sampling scheme. The problem of estimating the parameters in two-phase sampling would be more complex when the non-response is observed on both study and auxiliary variables. The problem of such situation was handled by Chaudhary and Kumar(2016). In order to demonstrate the theoretical facts, we have considered two different sets of empirical data
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