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Quantile Optimization Problem with Incomplete Information

A stochastic optimization problem with incomplete information is considered. Optimal solutions are selected using the minimax quantile criterion. This problem is closely connected with a confidence estimation problem for a random vector with incompletely known distribution. Generalized confidence regions are used as confidence estimates for a statistically uncertain vector. The quantile stochastic optimization problem under incomplete information is solved by means of an optimal choice of a generalized confidence region.
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