A Bahadur-Kiefer Theorem beyond the Largest Observation

✍ Scribed by J.H.J. Einmahl

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 251 KB
• Volume: 55
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1995.1065

✦ Synopsis

It is shown that under natural extreme-value conditions a distributional Bahadur-Kiefer theorem holds in a point lying outside the sample. The limiting distribution is degenerate if the extreme-value index is equal to one; the proper refinement for that case is also established. In both cases the limiting distribition is chi-square with one degree of freedom. 1995 Academic Press. Inc.