Abstract
In this chapter, we study the empirical Bayes estimation of the mean lifetime θ in an exponential distribution with unequal sample sizes. It is assumed that θ is in the interval [a,b] where 0 < a < b < ∞. We investigate a method for constructing an empirical Bayes estimator ϕ*n+1,n under unequal sample sizes situation. The asymptotic optimality of ϕ*n+1,n is studied. We have proved that ϕ*n+1,n is asymptotically optimal, and its regret converges to zero at a rate O ((ln n)3M−1/n) when both a and b are known, or at a rate O ((ln n)3M−1 (ln ln n)2/n) when both a and b are unknown, where M is an upper bound of sample sizes.
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© 2005 Birkhäuser Boston
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Liang, T. (2005). Empirical Bayes Estimation of Mean Lifetime for an Exponential Distribution: Unequal Sample Sizes Case. In: Balakrishnan, N., Nagaraja, H.N., Kannan, N. (eds) Advances in Ranking and Selection, Multiple Comparisons, and Reliability. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4422-9_17
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DOI: https://doi.org/10.1007/0-8176-4422-9_17
Publisher Name: Birkhäuser Boston
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