Unimprovable Solution to Systems of Empirical Linear Algebraic Equations
Probability
2007-05-23 v1
Abstract
An optimum solution free from degeneration is found to the system of linear algebraic equations with empirical coefficients 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 coefficient matrix and length of the right-hand side vector. Empirical coefficients and 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.
Keywords
Cite
@article{arxiv.math/0212375,
title = {Unimprovable Solution to Systems of Empirical Linear Algebraic Equations},
author = {A. V. Serdobolski},
journal= {arXiv preprint arXiv:math/0212375},
year = {2007}
}