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Sequential determination of estimator as well as sample size. (English) Zbl 0544.62075
Consider the problem of sequential estimation of the location parameter \(\theta\) of a symmetric distribution F with density f. The author obtains an adaptive sequential point estimator as well as a confidence interval for \(\theta\) which are asymptotically efficient with respect to the procedures that use the best trimmed mean as estimator and the best sample size for that trimmed mean.
The adaptive estimator as well as the stopping rules are obtained through minimizing the sample variances of \(\alpha\)-trimmed means, \(\alpha \in(0,{1\over2})\). The assumptions imposed on F and f are mild and involve existence of continuous derivatives of \(F^{-1}\) and f. However, the stopping rules proposed may require heavy computation.
Reviewer: C.Srinivasan

62L12 Sequential estimation
62F25 Parametric tolerance and confidence regions
62F35 Robustness and adaptive procedures (parametric inference)
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