Sequential estimation of the mean of NEF-PVF distributions |
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| Institution: | 1. School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, P.R. China;2. Center for System Reliability and Safety, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, P.R. China;1. Department of Information Systems, Faculty of Management, University of Tehran, Tehran, Iran;2. Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, Australia;1. School of Information, Zhejiang University of Finance and Economics, Hangzhou 310018, Zhejiang, China;2. Institute of Systems Engineering, Macau University of Science and Technology, Macau 999078, China;3. School of Computer, Liaocheng University, Liaocheng 252000, Shandong, China |
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| Abstract: | 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 ϵ F, 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. |
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