Asymptotics of conditional empirical processes (Q1109453)

The authors investigate asymptotic approximations of estimators of the conditional empirical process of Y given \(X=x\), leading to a functional law of the iterated logarithm. Two estimators are considered, a kernel- type estimator and a nearest-neighbor type estimator. The main results show that the weak behaviour of the conditional empirical processes at a given x is essentially the same as that of the empirical process, although the rates now depend on the bandwidth.