Unimprovable solution to systems of empirical linear algebraic equations

✍ Scribed by A.V Serdobolskii

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 96 KB
• Volume: 60
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(02)00148-7

✦ Synopsis

An optimum solution, free from degeneration, is found for a system of linear algebraic equations with empirical coe cients and right-hand sides. The quadratic risk of estimators of the unknown solution vector is minimized over a class of linear systems with given square norm of the coe cient matrix and length of the vector on the right-hand side. Empirical coe cients and the right-hand sides are assumed to be independent and normal with known variance. It is found that the optimal estimator has the form of a regularized minimum square solution with an extension multiple. A simple formula is derived showing explicitly the dependence of the minimal risk on parameters.