On a sequential rule for estimating the location parameter of an exponential distribution

A. P. Basu

Naval Research Logistics Quarterly, 1971, vol. 18, issue 3, 329-337

Abstract: Let us assume that observations are obtained at random and sequentially from a population with density function In this paper we consider a sequential rule for estimating μ when σ is unknown corresponding to the following class of cost functions \documentclass{article}\pagestyle{empty}\begin{document}$$ f\left(x\right) = \frac{1}{\sigma }e^{ - \left({\frac{{x - \mu }}{\sigma }} \right)},\,x >\mu,\, \ge 0,\sigma > 0. $$\end{document} In this paper we consider a sequential rule for estimating μ when σ is unknown corresponding to the following class of cost functions \documentclass{article}\pagestyle{empty}\begin{document}$$ C_N = A|\delta (X_1 ,...,X_N ) - \mu |^p + N $$\end{document} Where δ(XI,…,XN) is a suitable estimator of μ based on the random sample (X1,…, XN), N is a stopping variable, and A and p are given constants. To study the performance of the rule it is compared with corresponding “optimum fixed sample procedures” with known σ by comparing expected sample sizes and expected costs. It is shown that the rule is “asymptotically efficient” when absolute loss (p=‐1) is used whereas the one based on squared error (p = 2) is not. A table is provided to show that in small samples similar conclusions are also true.

Date: 1971
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https://doi.org/10.1002/nav.3800180305

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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:18:y:1971:i:3:p:329-337

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