Bahadur Representation of Nonparametric M-Estimators for Spatial Processes

Jia Chen*, Degui Li, Li Xin Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

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

Keywords

  • 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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