Invariant nonnegative minimum norm quadratic estimator of variance components and its application

Abstract

Minimum norm quadratic estimators were introduced by C. R. Rao in the 70's to attempt to give an unified approach to variance component estimation. One such estimator, which is called invariant nonnegative minimum norm quadratic, was proposed but not explicitly determined. In this paper, a fnormal solution to the invariant nonnegative minimum norm quadratic estimator is presented and then applied to some special cases.

AMS 1980 subject classifications::

• Primary 62H12
• secondary 62F10

Keywords:

• Variance component
• MINQE
• invariance
• nonnegativity
• closed convex cone
• orthogonal decomposition