Local Linear M-estimation in non-parametric spatial regression

Zhengyan Lin; Degui Li; Jiti Gao

doi:10.1111/j.1467-9892.2009.00612.x

Local Linear M-estimation in non-parametric spatial regression

Zhengyan Lin, Degui Li, Jiti Gao^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	286-314
Number of pages	29
Journal	Journal of Time Series Analysis
Volume	30
Issue number	3
DOIs	https://doi.org/10.1111/j.1467-9892.2009.00612.x
Publication status	Published - May 2009

Keywords

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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10.1111/j.1467-9892.2009.00612.x

http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9892.2009.00612.x/abstract

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title = "Local Linear M-estimation in non-parametric spatial regression",

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.",

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author = "Zhengyan Lin and Degui Li and Jiti Gao",

year = "2009",

month = may,

doi = "10.1111/j.1467-9892.2009.00612.x",

language = "English",

volume = "30",

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journal = "Journal of Time Series Analysis",

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TY - JOUR

T1 - Local Linear M-estimation in non-parametric spatial regression

AU - Lin, Zhengyan

AU - Li, Degui

AU - Gao, Jiti

PY - 2009/5

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AB - 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.

KW - marginal integration

KW - KERNEL DENSITY-ESTIMATION

KW - primary 62G07

KW - spatial process

KW - consistency

KW - ROBUST ESTIMATION

KW - secondary 60F05

KW - RANDOM-FIELDS

KW - VARIABLE BANDWIDTH

KW - local linear M-estimator

KW - alpha-mixing

KW - asymptotic normality

KW - ADDITIVE-MODELS

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U2 - 10.1111/j.1467-9892.2009.00612.x

DO - 10.1111/j.1467-9892.2009.00612.x

M3 - Article

SN - 0143-9782

VL - 30

SP - 286

EP - 314

JO - Journal of Time Series Analysis

JF - Journal of Time Series Analysis

IS - 3

ER -

Local Linear M-estimation in non-parametric spatial regression

Abstract

Keywords

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