Kernel density estimation for spatial processes: The L1 theory

Marc Hallin; Zudi Lu; Lanh T. Tran

doi:10.1016/S0047-259X(03)00060-5

Kernel density estimation for spatial processes: The L₁ theory

Marc Hallin
, Zudi Lu
, Lanh T. Tran

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

68 Citations (Scopus)

Abstract

The purpose of this paper is to investigate kernel density estimators for spatial processes with linear or nonlinear structures. Sufficient conditions for such estimators to converge in L₁ are obtained under extremely general, verifiable conditions. The results hold for mixing as well as for nonmixing processes. Potential applications include testing for spatial interaction, the spatial analysis of causality structures, the definition of leading/lagging sites, the construction of clusters of comoving sites, etc. © 2003 Elsevier Science (USA). All rights reserved.

Original language	English
Pages (from-to)	61-75
Journal	Journal of Multivariate Analysis
Volume	88
Issue number	1
DOIs	https://doi.org/10.1016/S0047-259X(03)00060-5
Publication status	Published - Jan 2004
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Bandwidth
Kernel density estimator
L1 theory
Spatial linear or nonlinear processes

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Cite this

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title = "Kernel density estimation for spatial processes: The L1 theory",

abstract = "The purpose of this paper is to investigate kernel density estimators for spatial processes with linear or nonlinear structures. Sufficient conditions for such estimators to converge in L1 are obtained under extremely general, verifiable conditions. The results hold for mixing as well as for nonmixing processes. Potential applications include testing for spatial interaction, the spatial analysis of causality structures, the definition of leading/lagging sites, the construction of clusters of comoving sites, etc. {\textcopyright} 2003 Elsevier Science (USA). All rights reserved.",

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AU - Hallin, Marc

AU - Lu, Zudi

AU - Tran, Lanh T.

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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N2 - The purpose of this paper is to investigate kernel density estimators for spatial processes with linear or nonlinear structures. Sufficient conditions for such estimators to converge in L1 are obtained under extremely general, verifiable conditions. The results hold for mixing as well as for nonmixing processes. Potential applications include testing for spatial interaction, the spatial analysis of causality structures, the definition of leading/lagging sites, the construction of clusters of comoving sites, etc. © 2003 Elsevier Science (USA). All rights reserved.

AB - The purpose of this paper is to investigate kernel density estimators for spatial processes with linear or nonlinear structures. Sufficient conditions for such estimators to converge in L1 are obtained under extremely general, verifiable conditions. The results hold for mixing as well as for nonmixing processes. Potential applications include testing for spatial interaction, the spatial analysis of causality structures, the definition of leading/lagging sites, the construction of clusters of comoving sites, etc. © 2003 Elsevier Science (USA). All rights reserved.

KW - Bandwidth

KW - Kernel density estimator

KW - L1 theory

KW - Spatial linear or nonlinear processes

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DO - 10.1016/S0047-259X(03)00060-5

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