On an Efficient Regression Type Estimator

Abstract

The regression type estimator proposed by KAUR (1985) is considered. Another expression for the approximated mean square error (AMSE), to a first degree of approximation, is obtained. This AMSE is also minimized with respect to a parameter α. Three numerical examples are included. These numerical examples show that this estimator is not significantly more efficient than regression estimator and with respect to ratio and sample mean estimators, it does not always exhibit a high efficiency, as was contended by KAUR (1985). Moreover, an upper bound for the relative precision of the proposed estimator with respect to linear regression estimator is derived.

An improved class of estimators for the population mean

“…Awareness of this should discourage any attempts to define new estimators, unless the practice of considering unbiased classes of estimators, or unbiased up to the first order of approximation, is overcome; on this see Kaur (1985); Jain (1987); Ganget and Prabhu-Ajgaonkar (1991); Rao (1991); Menéndez and Reyes (1998); Gupta and Shabbir (2008) and Koyuncu and Kadilar (2010).…”