Local linear spatial regression

By Marc Hallin, Zudi Lu, Lanh Tat Tran. 2004

162 citations recorded by the source corpus.

A local linear kernel estimator of the regression function x → g(x):= E[Y i |X i = x], x ∈ R d , of a stationary (d + 1)-dimensional spatial process {(Y i , X i ), i ∈ Z N } observed over a rectangular domain of the form in:= {i = (i 1 ,..,i N ) ∈ Z N |1 ≤ i k ≤ n k , k = 1,...,N}, n = (n 1 ,...,n N ) ∈ Z N , is proposed and investigated. Under mild regularity assumptions, asymptotic normality of the estimators of g(x) and its derivatives is established. Appropriate choices of the bandwidths are proposed. The spatial process is assumed to satisfy some very general mixing conditions, generalizing classical time-series strong mixing concepts. The size of the rectangular domain in is allowed to tend to infinity at different rates depending on the direction in Z N .

Subfields: Applied Mathematics, Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c219a995780de044febc59dc98676c5fadec7819

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Citations in the corpus

Nonparametric Spatial Prediction (2004, background): “Observe moreover that when (H3) holds with D = 0 (as it is usually assumed in the context of spatial regression, see [ 9 ]), then (H2) holds as soon as (H1) holds.”
Local linear spatial quantile regression (2009, methodology): “As in [24], two distinct forms (either (A3) and (A3′) or (A3) and (A3′′)) of spatial mixing are considered.”
Estimation in semiparametric spatial regression (2006, methodology): “The asymptotic normality of the kernel density estimator was also established for spatial linear processes by Hallin, Lu and Tran [14].”
Kernel regression estimation for continuous spatial processes (2007, methodology): “Except some papers, Biau and Cadre [5], Lu and Chen [33, 34], Hallin, Lu, and Tran [27], Carbon, Francq, and Tran [12], little attention has been paid to estimate spatial regression functions nonparametrically.”
Model-based mean square error estimators for k-nearest neighbour predictions and applications using remotely sensed data for forest inventories (2009, unknown): “; m = 0;1;2; N ðA4Þ where zjj′=zj−zj′,K is the bisquare kernel (Hallin et al., 2004), h is a kernel bandwidth, (hm=e1/(3min(4,q)×hm−1), Sm=(Iq×q+ρm−2β̂m−1β̂′m−1)1/2 is a q×q matrix that shrinks zij in directions of β̂m and stretches it in directions orthogonal to β̂m, and ρm=e−1/6ρm−1 is an…”
Asymptotic theory for nonparametric regression with spatial data (2011, methodology): “In a spatial context, nonparametric regression has been discussed by, for example, Tran and Yakowitz (1993), Hallin, Lu and Tran (2004a) .”