Annals of the Institute of Statistical Mathematics

, Volume 34, Issue 3, pp 545–558

# Locating the minimum of a function when the errors of observation have unknown density

• Thomas E. Obremski
Article

## 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  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.

## Keywords

Asymptotic Normality Stochastic Approximation Unknown Density Random Variable Versus Measurable Random Variable

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