Bahadur Representation of Nonparametric M-Estimators for Spatial Processes

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JournalActa mathematica sinica-English series
DatePublished - 1 Nov 2008
Issue number11
Volume24
Number of pages12
Pages (from-to)1871-1882
Original languageEnglish

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 h(n) = O(vertical bar n vertical bar(-1/5)), n epsilon 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(vertical bar n vertical bar(-4/5) log vertical bar n vertical bar). Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.

    Research areas

  • strongly mixing, Bahadur representation, RANDOM-FIELDS, LOCAL M-ESTIMATOR, TIME-SERIES, MODELS, local linear M-estimator, REGRESSION, spatial processes, DENSITY-ESTIMATION

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