Numerical methods for solving a class of matrix equations arising from inference for ranked set sampling on imperfect ranking

In this paper, we investigate some numerical methods for a class of matrix equations with constraints arising from inference for ranked set sampling on imperfect ranking. Based on the structure of the matrix equation, two classes of numerical methods are studied to solve the problem. The first idea is to treat the problem as a simplified Riccati equation, then a Schur method and a square-root method are derived. The second idea is entirely novel, which is based on an extended Krylov subspace originated from the doubly stochastic property of the related matrices. The performance and efficiency of all the numerical solvers are verified by numerical examples.