Approximate confidence intervals on linear combinations of expected mean squares

Abstract

Let represent independently distributed chi-squared random variables with n_i degrees of freedom. In this article, we develop new procedures for obtaining approximate confidence intervals on linear combinations of the θ_i . The proposed approximations are indexed by a “tuning” constant. By choosing the appropriate constant, which can be easily determined from data, we show that the proposed methods produce confidence intervals that maintain the stated confidence level. Numerical examples compare the performance to other approximations.

Keywords:

• Coverage Probabilities
• rāndom models
• simulation
• variance components