Locating the minimum of a function when the errors of observation have unknown density
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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  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.
KeywordsAsymptotic Normality Stochastic Approximation Unknown Density Random Variable Versus Measurable Random Variable
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