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Local Linear M-estimation in non-parametric spatial regression

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Publication details

JournalJournal of Time Series Analysis
DatePublished - May 2009
Issue number3
Volume30
Number of pages29
Pages (from-to)286-314
Original languageEnglish

Abstract

A robust version of local linear regression smoothers augmented with variable bandwidths is investigated for dependent spatial processes. The (uniform) weak consistency as well as asymptotic normality for the local linear M-estimator (LLME) of the spatial regression function g(x) are established under some mild conditions. Furthermore, an additive model is considered to avoid the curse of dimensionality for spatial processes and an estimation procedure based on combining the marginal integration technique with LLME is applied in this paper. Meanwhile, we present a simulated study to illustrate the proposed estimation method. Our simulation results show that the estimation method works well numerically.

    Research areas

  • marginal integration, KERNEL DENSITY-ESTIMATION, primary 62G07, spatial process, consistency, ROBUST ESTIMATION, secondary 60F05, RANDOM-FIELDS, VARIABLE BANDWIDTH, local linear M-estimator, alpha-mixing, asymptotic normality, ADDITIVE-MODELS

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