Modified Classes of Regression-Type Estimators of Population Mean in the Presence of Auxiliary Attribute under Double Sampling Scheme

Abstract

In sample survey, reliable and efficient estimates are often obtained using information from auxiliary variables during estimation and designing stages. However, there are times when the auxiliary information is attribute-based. Some authors have proposed estimators  using auxiliary attribute information when the population mean of auxiliary attribute is unknown. However, the estimators are ratio- based estimators which are less efficient when the bi-serial correlation between the study variable and the auxiliary attribute is negative.  In this study, regression approach was used to modify estimator d ZKi t to produce estimators that can be used for both negative and  positive correlation. In addition, another existing estimator was also modified to produce an estimator that is independent of an  unknown population parameter. The Biases and Mean Squared Errors (MSEs) of the modified estimators were determined using the  Taylor series approach up to the first order of approximation. The proposed estimators’ efficiency conditions over some existing  estimators were established. Empirical investigations were done using stimulation study and the results revealed that proposed  estimators have the lowest MSEs and the highest PREs of all the competing estimators and therefore can give better estimates of the  population mean. Therefore, it can be concluded that proposed estimators have better predictive power for estimating population mean  under two-phase sampling scheme.