A Note on Scheffé's Confidence Intervals

Abstract

It is commonly known that there is a relationship between (1) Scheffé's simultaneous confidence intervals on estimable linear functions of β, the vector of parameters in a linear model, and (2) the F test concerning a linear hypothesis on β. This relationship is utilized to identify a set of linearly independent best linear unbiased estimators of estimable functions of β that are influential contributors to the significance of the F test.

Key Words:

• Best linear unbiased estimator
• Estimable linear function
• Influential set
• Linear model
• Simultaneous confidence intervals