Concentration Probabilities for Restricted and Unrestricted MLEs

✍ Scribed by Manabu Iwasa; Yoshiya Moritani

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 153 KB
• Volume: 80
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.2000.1971

✦ Synopsis

We consider estimating the mean % of an n dimensional normal vector X with the restriction that % belongs to a closed convex set C. We investigate concentration probabilities for the restricted MLE ?(X | C) and the MLE X. When n=2, we prove the inequality P % [X # A+%] P % [?(X | C) # A+%] for any % # C and any closed convex and centrally symmetric set A. We discuss some extensions for n 3.