Summary
In considering the problem of locating the point θ at which a functionf achieves its minimum (or maximum) using the Kiefer-Wolfowitz (KW) stochastic approximation procedure, Abdelhamid [1] has shown that if the densityg of the errors obtained in estimating functional values is known, then a transformation of observations leads to methods which under mild conditions have desirable asymptotic properties. We address the more general problem of locating the point of minimum of a function wheng is unknown to the experimenter. In the procedure given in Theorem 4.1 we obtain the same asymptotic results as Abdelhamid in his version of the KW procedure.
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Obremski, T.E. Locating the minimum of a function when the errors of observation have unknown density. Ann Inst Stat Math 34, 545–558 (1982). https://doi.org/10.1007/BF02481053
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DOI: https://doi.org/10.1007/BF02481053