Abstract:
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We provide a weighting method of multivariate data for making a ranking. The weight is determined in such a way that the index has positive correlation with all variables, where each variable is assumed to have the meaning that a larger value indicates higher score. The weighted sum is called the objective general index. Mathematically, the problem of finding the weight is equivalent to a diagonal scaling problem. Numerical values of them are obtained via convex optimization. The method is also explained by a factor model with special loading structure. Generalizations of the index to ordered categorial data and a separation problem are discussed.
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