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Recursive estimates of quantile based on 0-1 observations. (English) Zbl 0764.62068
Summary: The objective of this paper is to introduce some recursive methods that can be used for estimating an \(LD\)-50 value. These methods can be used more generally for the estimation of the \(\gamma\)-quantile of an unknown distribution provided we have 0-1 observations at our disposal. Standard methods based on the Robbins-Monro procedure are introduced together with different approaches of C. F. J. Wu [J. Am. Stat. Assoc. 80, 974- 984 (1985; Zbl 0588.62133)] or H. G. Mukerjee [Ann. Stat. 9, 1020- 1025 (1981; Zbl 0478.62069)]. Several examples are also mentioned in order to demonstrate the usefulness of the methods presented.
62L20 Stochastic approximation
62P10 Applications of statistics to biology and medical sciences; meta analysis
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