IMPROVED ESTIMATION UNDER MIDZUNO – LAHIRI – SEN TYPE SAMPLING SCHEME

Abstract

The generalized ratio type estimator for estimating the mean or total of finite population proposed by Walsh (1970) is reconsidered following Midzuno-Lahiri-Sen type sampling scheme. The unbiasedness of the generalized ratio estimator under the proposed Midzuno-Lahiri-Sen type sampling scheme is established and the expression of mean square error of the generalized ratio estimator under the proposed Midzuno-Lahiri-Sen type sampling scheme is derived. Further the optimum value of the parameter involved and the minimum mean square error under this optimum value of the parameter are also given. A comparative study of the proposed sampling strategy as compared to mean per unit estimator, ratio estimator, product estimator, linear regression estimator and generalized ratio estimator (Walsh) is made. The concluding remarks show that using suitable range information we can get estimators which under the proposed Midzuno-Lahiri-Sen type sampling scheme are better than the usual mean per unit estimator, ratio estimator, product estimator, linear regression estimator and generalized ratio estimator (Walsh) in the sense of unbiasedness and smaller mean square error. Finally an empirical study is included for illustration.