Spectral theory of minimax estimation (Q1914883)

Sometimes the task of estimating parameters of systems of equations can be reduced to finding the minimal value of the maximal eigenvalue on a definite set of numbers. Many works have been published where the tasks of estimating are considered. In these proceedings, the estimates of equations parameters are obtained by means of the spectral theory of linear operators. Therefore, such estimates are called spectral \(S\)-estimates. Here, the set of \(S_1\)-estimates of solutions of systems of linear equations with random parameters is found. It is proved that the maximal eigenvalue in the goodness criterion is not simple. For the purpose of finding estimates from the \(S_1\) set, the perturbation formulas for eigenvalues and formulas for distribution density of random matrices are used.