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.