Construction of Prediction Intervals in Location-Scale Families

✍ Scribed by Debashis Kushary

• Book ID: 102761359
• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 764 KB
• Volume: 38
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710380712

✦ Synopsis

Let X I 5 x2 5 g ... 5 x, be the r smallest observations out of n observations from a location-scale family with density a f r?) where p and u are the location and the scale parameten respectively.

The goal is to construct a prediction interval of the form @ + k16, ji + k26) for a location-scale invariant function, T(!! = T(Y1. ..., Y , , of m future observations from the same distribution. Given any invariant estimators ji and 6, we have developed a general procedure for how to compute the values of kl and k2. The two attractive features of the procedure are that it does not require any distributional knowledge of the joint distribution of the estimators beyond their first two raw moments and j2 and b can be any invariant estimatom of p and u. Examples with real data have been given and extensive simulation study showing the performance of the procedure is also offered.