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A note on accelerated sequential estimation of the mean of NEF-PVF distributions
Arup Bose,Nitis Mukhopadhyay +1 more
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In this paper, an accelerated version of the full purely sequential methodology of Bose and Boukai (1993b, submitted) is proposed along the lines of Mukhopadhyay (1993a, Tech Report, No 93-27, Department of Statistics, University of Connecticut) in order to achieve operational savings.Abstract:
The minimum risk point estimation for the mean is addressed for a natural exponential family (NEF) that also has a power variance function (PVF) under a loss function given by the squared error plus linear cost An appropriate accelerated version of the full purely sequential methodology of Bose and Boukai (1993b, submitted) is proposed along the lines of Mukhopadhyay (1993a, Tech Report, No 93-27, Department of Statistics, University of Connecticut) in order to achieve operational savings The main result provides the asymptotic second-order expansion of the regret function associated with the accelerated sequential estimator of the population meanread more
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Journal ArticleDOI
An accelerated bias-corrected sequential estimation for the mean of NEF-PVF distributions
Benzion Boukai,Jyotirmoy Sarkar +1 more
TL;DR: In this paper, an accelerated sequential procedure for estimating the mean p in the class of the natural exponential family of distributions having power variance function (NEF-PVF) is proposed.
References
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Book
Information and Exponential Families in Statistical Theory
TL;DR: In this article, the information and exponential families in statistical theory were studied. But they did not consider the exponential family in the context of exponential families. And they were not considered in this paper.
Journal ArticleDOI
Natural Exponential Families with Quadratic Variance Functions
TL;DR: The normal, Poisson, gamma, binomial, and negative binomial distributions are univariate natural exponential families with quadratic variance functions as mentioned in this paper, where the variance is at most a function of the mean.
Book
Nonlinear Renewal Theory in Sequential Analysis
TL;DR: Randomly Stopped Sequences Random Walks The Sequential Probability Ratio Test Nonlinear Renewal Theory Local Limit Theorems Open-Ended Tests Repeated Significance Tests Multiparameter Problems Estimation Following Sequential Testing Sequential Estimation as mentioned in this paper.
Journal ArticleDOI
Second Order Approximations for Sequential Point and Interval Estimation
TL;DR: In this paper, the authors find the asymptotic distribution of the excess $R_c = ct_c^\alpha -S_n 1, L(n)$ as $c \rightarrow 0$ and apply their results to obtain second order approximations to the expected sample size and risk of some sequential procedures for estimation.