Sequential estimation of the mean of NEF-PVF distributions

Bose, A. ; Boukai, Benzion (1997) Sequential estimation of the mean of NEF-PVF distributions Journal of Statistical Planning and Inference, 63 (1). pp. 55-70. ISSN 0378-3758

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Let F = {F0: 0 ε θ} denote the class of natural exponential family of distributions having power variance function, (NEF-PVF). We consider the problem of sequentially estimating the mean µ of F0 εF, based on i.i.d. observations from F0. We propose an appropriate sequential estimation procedure under a combined loss of estimation error and sampling cost. We provide expansion for the regret Ra and study its asymptotic properties. We show that Ra = cv2(μ) + o(1) as a →∞, where c>0 is a known constant and v(μ) denotes the coefficient of variation of F0.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Sequential Estimation; Stopping Time; Regret Expansion; Exponential Families; Power Variance Function; Compound Poisson; Stable Distributions
ID Code:5464
Deposited On:18 Oct 2010 10:10
Last Modified:20 May 2011 10:58

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