Bilinear quantile optimization: A numerical algorithm

The extremum point of the sample estimate of the quantile function is tak en to be the estimate for the solution of the quantile optimization problem having a bilinear loss function. A statistical analog of the generalized minimax approach is developed for representing the sample estimate of the quantile function, in minimax fern. The search: far the point of extremum of the sample estimate of the quantile function is reduced to an, equivalent minimax: problem. The minimax problem is solved by sequentially solving a finite number of linear programming problems. The results are illustrated by a numerical example.