A Simple Correlation Adjustment Procedure Applied to Confidence Interval Construction

Abstract

The assumption of approximate normality of a pivotal used for constructing confidence intervals or tests often is violated by a substantial correlation between the point estimator at hand and the estimator of its variance. This can be caused by underlying skewness of data, generating both bias and skewness of the pivotal and leading to, for example, confidence intervals with poorer coverage properties, especially for one-sided intervals. We present in a general setting a simple, yet effective procedure that takes into account this correlation and leads to alternative adjusted intervals with more appealing coverage properties. We provide examples, including a simulation study.

Keywords:  :

• Confidence interval
• Correlation
• Pivotal
• Skewness