Minimax Risk Inequalities for the Location–Parameter Classification Problem

✍ Scribed by Pieter C. Allaart

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 275 KB
• Volume: 66
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1998.1748

✦ Synopsis

Minimax risk inequalities are obtained for the location-parameter classification problem. For the classical single observation case with continuous distributions, best possible bounds are given in terms of their Le vy concentration, establishing a conjecture of Hill and Tong (1989). In addition, sharp bounds for the minimax risk are derived for the multiple (i.i.d.) observations case, based on the tail concentration and the Le vy concentration. Some fairly sharp bounds for discontinuous distributions are also obtained.