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August 2001 Density estimation for spatial linear processes
Marc Hallin, Zudi Lu, Lanh Tat Tran
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Bernoulli 7(4): 657-668 (August 2001).


The problem of estimating the marginal densities of a spatial linear process, observed over a grid of $\mathbb {Z}^N$, is considered. Under general conditions, kernel density estimators computed at any $k$-tuple of sites are shown to be asymptotically multivariate normal. Their limiting covariance matrix is also computed. Despite the huge development of nonparametric estimation methods in the analysis of time series data, little has so far been done to introduce them into the context of random fields. The generalization indeed is far from trivial since the points of $\mathbb {Z}^N$ do not have a natural ordering when $N>1$. No mixing conditions are required, but linearity is assumed.


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Marc Hallin. Zudi Lu. Lanh Tat Tran. "Density estimation for spatial linear processes." Bernoulli 7 (4) 657 - 668, August 2001.


Published: August 2001
First available in Project Euclid: 17 March 2004

zbMATH: 1005.62034
MathSciNet: MR2002I:62080

Keywords: bandwidth , Density estimation , ‎kernel‎ , spatial process

Rights: Copyright © 2001 Bernoulli Society for Mathematical Statistics and Probability


Vol.7 • No. 4 • August 2001
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