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Nonparametric regression estimation for random fields in a fixed-design

Mohamed El Machkouri
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Abstract

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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Mohamed El Machkouri. 2005-02-04. Nonparametric regression estimation for random fields in a fixed-design. https://arxiv.org/abs/math/0502091

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