Abstract

In a multivariate stratified population where more than one characteristics are defined on each unit of the population the use of individual optimum allocations is not feasible. A compromise criterion is needed to workout an allocation which is optimum for each characteristic in some sense. If the problem of nonresponse is also there then the precision of the estimate is further reduced. Khare (1987) discussed the problem of optimum allocation in stratified sampling in presence of nonresponse for fixed cost as well as for fixed precision of the estimate for univariate case. Khan et al. (2008) extended the same for multivariate population and worked out a compromise allocation using Lagrange Multiplier technique. Most of the authors minimize some function of the variances of the estimators under cost restrictions. If the units of easurement of various characteristics are not same the minimization of some function of variances does not make sense. In the present paper we minimize the weighted sum of squared coefficient of variations under the cost and other restriction. The resulting problem of working out a compromise allocation in presence of nonresponse turns out to be an All Integer Nonlinear Programming Problem. Under certain assumption this problem is solved by the Lagrange Multipliers Technique and explicit formulas are obtained for sample sizes for the first and the second attempts. A numerical illustration is given to demonstrate the suitability of the proposed criterion.

Author: Rahul Varshney, Najmussehar and M. J. Ahsan

Received on: October, 2011

Accepted on: November, 2011