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Nonparametric sequential estimation of zeros and extrema of regression functions

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Let(X,Y), (X_{l}, Y_{l}), (X_{2}, Y_{2}), cdotsbe independent identically distributed pairs of random variables, and letm(x)=E(Y|X = x)be the regression curve ofYonX. The estimation of zeros and extrema of the regression curve via stochastic approximation methods is considered. Consistency results of some sequential procedures are presented and termination rules are defined providing fixed width confidence intervals for the parameters to be estimated.

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Information Theory, IEEE Transactions on  (Volume:33 ,  Issue: 3 )