MINIMAX ESTIMATION IN LINEAR-REGRESSION WITH SINGULAR COVARIANCE STRUCTURE AND CONVEX POLYHEDRAL CONSTRAINTS

Let the parameter of the linear regression model be restricted to a compact and convex polyhedron. On the basis of this additional information an estimator is shown to exist which minimizes the maximal weighted risk. This exact minimax solution turns out to be not feasible, but can be characterized as a limit point of approximate and operational minimax solutions. The results obtained are valid for general quadratic loss and possibly singular covariance matrix.