Nonparametric regression estimation for random fields in a fixed-design

Details Nonparametric regression estimation for random fields in a fixed-design Nonparametric regression estimation for random fields in a fixed-design

2005-02-04

arxiv.org/abs/math/0502091v1

Mathematics

Statistics Theory

Accept\'{e} pour publication dans la revue "Statistical Inference for Stochastic Processes"

Scientific paper

We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These estimators can attain the optimal rates of uniform convergence and the results apply to a large class of random fields which contains martingale-difference random fields and mixing random fields.

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