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An Optimum Multivariate Stratified Sampling Design with Nonresponse: A Lexicographic Goal Programming Approach

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Journal of Mathematical Modelling and Algorithms

Abstract

In a multivariate stratified sample survey with L strata and p > 1 characteristics, defined on each unit of the population, let the estimation of all the p-population means be of interest. As discussed by Cochran (1977), since the optimum allocation for one characteristic will not in general be optimum for other characteristics some compromise must be reached in a multiple characteristics stratified surveys. Various authors worked out allocations that are based on a compromise criterion. The resulting allocations are optimal for all characteristics in some sense, for example an allocation that minimizes the trace of the variance-covariance matrix of the estimators of the population means or an allocation that minimizes the weighted average of the variances or an allocation that maximizes the total relative efficiency of the estimators as compared to the corresponding individual optimum allocations. In the present paper the problem of optimum allocation in multivariate stratified random sampling in the presence of nonresponse has been formulated as a multiobjective integer nonlinear programming problem and a solution procedure is developed using goal programming technique. Three numerical examples are worked out to illustrate the computational details. A comparison of the proposed method with some well known methods is also carried out to show the practical utility of the proposed method.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, 202002, India

    Rahul Varshney & M. J. Ahsan

  2. School of Computing, Information and Mathematical Sciences, University of the South Pacific, Suva, Fiji

    M. G. M. Khan

Authors
  1. Rahul Varshney
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  2. M. J. Ahsan
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  3. M. G. M. Khan
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Correspondence to M. G. M. Khan.

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Varshney, R., Ahsan, M.J. & Khan, M.G.M. An Optimum Multivariate Stratified Sampling Design with Nonresponse: A Lexicographic Goal Programming Approach. J Math Model Algor 10, 393–405 (2011). https://doi.org/10.1007/s10852-011-9164-2

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  • DOI: https://doi.org/10.1007/s10852-011-9164-2

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