Asymptotics of conditional empirical processes. (English) Zbl 0655.62040
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.
Reviewer: Z.Rychlik
MSC:
| 62G05 | Nonparametric estimation |
| 60F17 | Functional limit theorems; invariance principles |
| 60F15 | Strong limit theorems |
Keywords:
conditional distribution; multivariate Wiener process; stochastic integrals; U-statistics; asymptotic approximations of estimators; functional law of the iterated logarithm; kernel-type estimator; nearest- neighbor type estimator; conditional empirical processes; bandwidthReferences:
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