Abstract
Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the so- called optimal bandwidth hn = O(|n| � 1 5), n ∈ Z d , is chosen, then the remainder rates in the Bahadur representation for the local M-estimators of the regression function and its derivative are of order O(|n| � 4 5 log |n|). Moreover, we derive some asymptotic properties for the nonparametric local linear
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