Abstract
In this paper, we have proposed three classes of mixture ratio estimators for estimating population mean by using information on auxiliary variables and attributes simultaneously in two-phase sampling under full, partial and no information cases and analyzed the properties of the estimators. A simulated study was carried out to compare the performance of the proposed estimators with the existing estimators of finite population mean. It has been found that the mixture ratio estimator in full information case using multiple auxiliary variables and attributes is more efficient than mean per unit, ratio estimator using one auxiliary variable and one attribute, ratio estimator using multiple auxiliary variable and multiple auxiliary attributes and mixture ratio estimators in both partial and no information case in two-phase sampling. A mixture ratio estimator in partial information case is more efficient than mixture ratio estimators in no information case.
Highlights
The history of using auxiliary information in survey sampling is as old as history of the survey sampling
The study variable and the auxiliary variable had a high positive correlation and the regression line was passing through the origin
We will extend the mixture ratio estimator proposed by Moeen, Shahbaz and Hanif [17] in single-phase sampling to two-phase sampling under full, partial and no information case strategies introduced by Samiuddin and Hanif [18] and incorporate Arora and Bansi [19] approach in writing down the mean squared error
Summary
The history of using auxiliary information in survey sampling is as old as history of the survey sampling. Sharma and Grover [11] used the information on auxiliary attributes in ratio estimator in estimating population mean of the variable of interest using known attributes such as coefficient of variation, coefficient kurtosis and point bi-serial correlation coefficient. The estimator had a smaller MSE compared to that of Jhajj, Sharma and Grover [11] They extended their work to ratio estimator which was generalization of Naik and Gupta [12] estimator in single- and double-phase samplings with full information, partial information and no information. Shahbaz and Hanif [17] proposed a class of mixture ratio and regression estimators for single-phase sampling for estimating population mean by using information on auxiliary variables and attributes simultaneously. We will extend the mixture ratio estimator proposed by Moeen, Shahbaz and Hanif [17] in single-phase sampling to two-phase sampling under full, partial and no information case strategies introduced by Samiuddin and Hanif [18] and incorporate Arora and Bansi [19] approach in writing down the mean squared error
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