Improved Ratio"type Estimator for Variance Using Auxiliary Information

Suppose we have a population of N identifiable units on which (k + 1) characteristics y, xJ, X2..." Xk are defined. Here y is the characteristic of interest and Xi. (i = 1, 2, ... , k) are auxiliary characteristics whose population variances or, (i =1,2, ... , k) are assumed to be known. Let (Yh, Xih) denote the values ofy and Xi on the unit h. Assume that a simple random sample of size n is drawn with replacement, (Yh, Xih), (h =1, 2, ...• n) are observed. Now assume that the problem is to estimate the population variance