Family of estimators of mean, ratio and product of a finite population using random nonresponse

In this paper a family of estimators for estimating mean, ratio and product of two means of a finite population are suggested and studied under the two different situations of random non-response considered by Tracy and Osahan (1994, Statistica 54(2):163–168), Singh and Joarder (1998, Metrika 47:241–249) and Singh et al. (2000, Statistica 60(1):39–44). Asymptotic expressions of biases and mean squared errors of the proposed families are derived. Optimum conditions are obtained under which the proposed families of estimators have the minimum mean squared error (MSE). Furthermore, the optimum values, depending upon population parameters, when replaced by sample values, yield the estimators having the minimum MSE of the optimum estimators. The estimators for MSEs of the suggested families are also given.