On an Optimization Problem Related to Statistical Investigations

Peter Bod

A chapter in Probability and Statistical Inference, 1982, pp 47-51 from Springer

Abstract: 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.

Date: 1982
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DOI: 10.1007/978-94-009-7840-9_6

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