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Multivariate Multi-Objective Allocation in Stratified Random Sampling: A Game Theoretic Approach

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There were no more view minimax solutions in sampling from finite populations , and she won help variations - which Iran is to go those resulting company and coach texts - will find in program until all complex's enterprises know designed seen. This can be viewed to be in the same vein of the representer theorem in machine learning. Titre : Minimax semi-supervised confidence sets for multi-class classification. Navigation Accueil. Plan du site. Second, we use standard weight vector W h 2 to solve minimax game, however, various other weight vector may be used for outer minimization problem.

The authors extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research group no RG National Center for Biotechnology Information , U.

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PLoS One. Published online Dec 9. Yong Deng, Editor. Author information Article notes Copyright and License information Disclaimer. Competing Interests: The authors have declared that no competing interests exist. Conceptualization: YSM. Data curation: YSM. Formal analysis: YSM. Funding acquisition: YSM. Investigation: YSM. Methodology: YSM. Project administration: AMS. Resources: AMS. Software: IH.

Supervision: YSM. Validation: IH. Writing — original draft: YSM. Received Apr 28; Accepted Nov This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abstract We consider the problem of multivariate multi-objective allocation where no or limited information is available within the stratum variance. Introduction A choice of sampling plan is fundamental to any statistical study because it provides estimates of population parameters. A detailed discussion given in [ 19 ] [ 20 — 22 ], [ 23 — 26 ], [ 27 — 30 ], [ 31 ] and [ 32 ] Second section explains the sampling notations.

Players: Sampler player 1 and Adversary player 2 If we consider sampler as player 1, the z jh from Eq 3 to be his loss in a zero-sum game against Adversary player 2 for characteristic j in the stratum h. Payoff matrix of Sampler player 1 While playing a zero sum game, each player try to optimize his gain or loss. Minimax game for allocation Assume that the sampler and the Adversary each choose a strategy. Solution of the allocation game The solution of the allocation problem can be formulated, as in previous section.

Numerical Illustration This idea of sample selection is applied on a real data of Master of Philosophy Table 1 induction into the department of Statistics, Quiad-e-Azam university Islamabad, Fall Open in a separate window. Computation of payoff matrix We use the model 6 to compute payoff matrix. Table 2 Payoff Matrix of sampler. Solution of minimax game For the outer segment of model 7 , we can use any suitable goal programming technique discussed in [ 22 , 23 , 28 ], [ 29 — 31 ], [ 34 ] and [ 35 ].

The Annals of Mathematical Statistics

Fig 1. Discussion on results We found for our referred example that the total weighted variation sum over characteristics in first stratum ranging from 0. Data Availability All relevant data are within the manuscript. References 1. Total survey error. Jossey-Bass Publishers; Cochran WG. Groves RM. Survey errors and survey costs. Kish L.

Simple Random Sampling : ExamSolutions Maths Revision

Survey Sampling. Optima and proxima in linear sample designs. Total survey design-application to a collection of the construction industry. Theory of games and statistical decisions Courier Corporation ; Aggarwal OP. The Annals of Mathematical Statistics. Ghosh JK. A game theory approach to the problem of optimum allocation in stratified sampling with multiple characters.

Calcutta Statistical Association Bulletin. Kokan A, Khan S. Optimum allocation in multivariate surveys: An analytical solution. Ericson WA. Optimum stratified sampling using prior information. Journal of the American Statistical Association.

Minimax solutions in sampling from finite populations - Semantic Scholar

Chatterjee S. Multivariate stratified surveys. Yates F, et al. Sampling methods for censuses and surveys. Effects of environment knowledge on agglomeration and cooperation in spatial public goods games. Advances in Complex Systems.

Dynamic instability of cooperation due to diverse activity patterns in evolutionary social dilemmas. EPL Europhysics Letters.