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On an Optimization Problem Related to Statistical Investigations

In: Probability and Statistical Inference

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  • Peter Bod

Abstract

G. Tusnády asked the following question: Given a finite yet large number of non-negative vectors: $${a_i} \in R_ + ^n(i = 1,2, \ldots ,m)$$ how is it possible to find a vector $$\hat x \in R_ + ^n{\text{ with }}\mathop {\rm Z}\limits_{j = 1}^n {\xi _j} = 1$$ such that the product of the scalar products of $$\hat x$$ with the given vectors becomes as large as possible. It is clear: $$\hat x$$ is also the vector for which the geometric mean of the scalar products will be maximum.

Suggested Citation

  • Peter Bod, 1982. "On an Optimization Problem Related to Statistical Investigations," Springer Books, in: Wilfried Grossmann & Georg Ch. Pflug & Wolfgang Wertz (ed.), Probability and Statistical Inference, pages 47-51, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-7840-9_6
    DOI: 10.1007/978-94-009-7840-9_6
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