A minimum matrix valued risk estimator combining restricted and ordinary least squares estimators

Abstract

In this article, attention is focused on the convex combination estimator, $\overline{\beta }=A\widehat{\beta }+(I-A){\widehat{\beta }}_R.$ We have proved that the matrix valued risk of the new convex matrix estimator cannot exceed the individual matrix valued risk of $\widehat{\beta }$ and ${\widehat{\beta }}_R.$

Keywords:

• Convex optimization
• mean square error
• ordinary least squares
• restricted least squares

Mathematics:

• Subject
• Classification: 46N10
• 47N10
• 62J05
• 62J07