The Relative Efficiency of Prediction Intervals

Abstract

There is extensive literature on the measurement of the relative efficiencies of estimators, hypothesis tests, and confidence intervals. However, the important topic of the measurement of the relative efficiencies of prediction intervals has hitherto not been properly explored. Following Hodges and Lehmann (1970), we require that a measure of the relative efficiency of two prediction intervals be stable in large samples. We examine the consequences of this requirement when these prediction intervals have coverage probability (a) equal to nominal and (b) asymptotically equal to nominal. Illustrations for independent and identically distributed data and time series data are provided.

Keywords:

• Prediction interval
• Relative efficiency

Mathematics Subject Classification:

• Primary 62M20
• Secondary 62F99, 62G99