Nonparametric regression estimation for random fields in a fixed-design. (English) Zbl 1110.62052
Summary: 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.
MSC:
| 62G08 | Nonparametric regression and quantile regression |
| 62M40 | Random fields; image analysis |
| 62G20 | Asymptotic properties of nonparametric inference |
Keywords:
kernel estimators; strong consistency; fixed-design; exponential inequalities; martingale difference random fields; mixing; Orlicz spacesReferences:
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