• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.629-634
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• 1998

As most of distributions appearing in applications are finite but with the unknown domain of finiteness, we propose to use the robust minimax approach for the determination of the boundaries of this domain. The obtained least favorable distribution minimizing Fisher information over the class of the approximately Gaussian finite distributions gives the reasonable sizes of the domain of finiteness and the thresholds of truncation.

• The Pure and Applied Mathematics
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• v.8 no.2
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• pp.79-85
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• 2001

As most Of distributions in applications have a finite support, we introduce the class of finite distributions with the known shape of their central part and the unknown tails. Furthermore, we use the Huber minimax approach to determine the unknown characteristics of this class. We obtain the least informative distributions minimizing Fisher information for location in the classes of the truncated Gaussian and uniform distributions, and these results give the reasonable values of the thresholds of truncation. The properties of the obtained solutions are discussed.

• Journal of Korea Water Resources Association
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• v.50 no.3
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• pp.191-200
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• 2017

A robust parameter set (ROPS) selection framework for an unsteady flow model was developed by combining Pareto optimums obtained by outcomes of model calibration using multi-site observations with the minimax regret approach (MRA). The multi-site calibration problem which is a multi-objective problem was solved by using an aggregation approach which aggregates the weighted criteria related to different sites into one measure, and then performs a large number of individual optimization runs with different weight combinations to obtain Pareto solutions. Roughness parameter structure which can describe the variation of Manning's n with discharges and sub-reaches was proposed and the related coefficients were optimized as model parameters. By applying the MRA which is a decision criterion, the Pareto solutions were ranked based on the obtained regrets related to each Pareto solution, and the top-rated one due to the lowest aggregated regrets of both calibration and validation was determined as the only ROPS. It was found that the determination of variable roughness and the corresponding standardized RMSEs at the two gauging stations varies considerably depending on the combinations of weights on the two sites. This method can provide the robust parameter set for the multi-site calibration problems in hydrologic and hydraulic models.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.289-298
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• 1999

We consider a minimax approach to make a design robust to many types or uncertainty arising in reality when dealing with non-normal linear models. We try to build a design to protect against the worst case, i.e. to improve the "efficiency" of the worst situation that can happen. In this paper, we especially deal with the generalized linear model. It is a known fact that the generalized linear model is a universal approach, an extension of the normal linear regression model to cover other distributions. Therefore, the optimal design for the generalized linear model has very similar properties as the normal linear model except that it has some special characteristics. Uncertainties regarding the unknown parameters, link function, and the model structure are discussed. We show that the suggested approach is proven to be highly efficient and useful in practice. In the meantime, a computer algorithm is discussed and a conclusion follows.