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Local Linear M‐estimation in non‐parametric spatial regression
Author(s) -
Lin Zhengyan,
Li Degui,
Gao Jiti
Publication year - 2009
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2009.00612.x
Subject(s) - mathematics , estimator , curse of dimensionality , asymptotic distribution , consistency (knowledge bases) , linear regression , parametric statistics , local regression , normality , statistics , mathematical optimization , polynomial regression , geometry
. 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.