Conditional Interval Estimation of the Ratio of Variance Components following Rejection of a Pre-test

Abstract

The conditional confidence interval for a ratio of variance components in the random effects model and the random effects nested design following a preliminary test is investigated. The conditional confidence interval (CCI) may be shorter than the unconditional confidence interval (UCI) in contrast to the findings for the mean of a normal distribution by Meeks and D'Agostino (1983). The conditional coverage probability of the UCI is obtained by computing the coverage probability under the conditional probability density function. It is shown that the conditional coverage pobability of the UCI is not uniformly greater than or less than the nominal level. The UCI is appropriate only when one does not perform any pre-test. However, if a pre-test is performed before the construction of a confidence interval, then the appropriate confidence interval is the CCI because the pre-test affects subsequent inference procedures.

Keywords::

• Conditional confidence interval
• truncated F distribution
• nested design
• preliminary test
• random effects model
• variance components