Unimprovable Solution to Systems of Empirical Linear Algebraic Equations

Details Unimprovable Solution to Systems of Empirical Linear Algebraic Equations Unimprovable Solution to Systems of Empirical Linear Algebraic Equations

2002-12-30

arxiv.org/abs/math/0212375v1

Elsevier Science, Statistics & Probability Letters, Volume 60 (1), p.1-6, 2002

Mathematics

Probability

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Unimprovable Solution to Systems of Empirical Linear Algebraic Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Unimprovable Solution to Systems of Empirical Linear Algebraic Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Unimprovable Solution to Systems of Empirical Linear Algebraic Equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-581182