Sequential estimation of the mean of NEF-PVF distributions

✍ Scribed by Arup Bose; Benzion Boukai

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 540 KB
• Volume: 63
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(96)00197-8

✦ Synopsis

ILet .F : {F;!: II E 0) denote the class of natural exponential family of distributions having power variance function, (NEF-PVF). WC consider the problem of' sequentially estimating the mean /L of 15 E .P, based on i.i.d. observations from 6,. WC propose an appropriate scclucntial estimation procedure under a combined loss of estimation error and sampling cost. We provide expansion for the regret .R, and study its asymptotic properties. We show that A+',, : &( // ) T o( I ) as (I -X. where c > 0 is a known constant and r(/l) denotes the coefficient of variation of I-Y,.