A Generalized Estimator for the Mean of a Finite Population Using Multi-Auxiliary Information

Abstract

For estimating the mean of a finite population using information on p auxiliary characters x₁, ···, x_p1 a class of ratio type estimators is considered. For any function h(u₁, ···, u_p) = h(u) where , the ratio of the simple random sample mean and the population mean of the character x_i, such that h(e) = 1, e_i = 1, i = 1, ···, p, and such that it satisfies the conditions (1), (2) and (3) of Section 3, the estimator considered is . Asymptotic expressions for the bias and the variance of the estimator are obtained and it has been shown that ratio estimators of the form are asymptotically no more efficient than the regression estimator.