Nonparametric sequential estimation of zeros and extrema of regression functions

Let
(X,Y), (X_{l}, Y_{l}), (X_{2}, Y_{2}), \cdots
be independent identically distributed pairs of random variables, and let
m(x)=E(Y|X = x)
be the regression curve of
Y
on
X
. 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.