Generalized P-phased Regression Estimators with Single and Two Auxiliary Variables

Farhan Hameed, Hina Khan

Abstract


Multiphase sampling has been the concept not being utilized is estimation of ratio and regression estimator widely. In the recent study we have proposed new dimension of sampling survey of estimations by proposing two generalized p-phase regression estimators with single and two auxiliary variables for estimating population mean. The proposed estimators are the generalized p-phase cases of Hanif et al (2015) and Hanif (2007) respectively. Both the estimators from which we took motivation are now special cases of our proposed estimators. We have derived unbiasedness, expression of Mean Square Errors along with family of estimators based upon p-phased generalization. We have derived expression of MSE in such a way that these expression can be used to obtained results for every phase we desire. By conducting empirical study on proposed estimators we have shown many situation in which MSE can be reduced by increasing number of phases. Hence, our study will open new horizon in the field of multiphase sampling where a lot of challenges are waiting to be resolved by proposing new estimators for phases above 2nd phase.


Keywords


MSE, NIC, Generalized P-Phased, Auxiliary Variable

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DOI: http://dx.doi.org/10.18187/pjsor.v13i3.1573

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Title

Generalized P-phased Regression Estimators with Single and Two Auxiliary Variables

Keywords

MSE, NIC, Generalized P-Phased, Auxiliary Variable

Description

Multiphase sampling has been the concept not being utilized is estimation of ratio and regression estimator widely. In the recent study we have proposed new dimension of sampling survey of estimations by proposing two generalized p-phase regression estimators with single and two auxiliary variables for estimating population mean. The proposed estimators are the generalized p-phase cases of Hanif et al (2015) and Hanif (2007) respectively. Both the estimators from which we took motivation are now special cases of our proposed estimators. We have derived unbiasedness, expression of Mean Square Errors along with family of estimators based upon p-phased generalization. We have derived expression of MSE in such a way that these expression can be used to obtained results for every phase we desire. By conducting empirical study on proposed estimators we have shown many situation in which MSE can be reduced by increasing number of phases. Hence, our study will open new horizon in the field of multiphase sampling where a lot of challenges are waiting to be resolved by proposing new estimators for phases above 2nd phase.


Date

2017-09-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 13 No. 3, 2017



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810