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Kernel density estimation for spatial processes: the L1 theory

✍ Scribed by Marc Hallin; Zudi Lu; Lanh T. Tran

Book ID
104269887
Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
199 KB
Volume
88
Category
Article
ISSN
0047-259X

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✦ Synopsis

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 L 1 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.

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In order to construct confidence sets for a marginal density f of a strictly stationary continuous time process observed over the time interval [0, T ], it is necessary to have at one's disposal a Central Limit Theorem for the kernel density estimator f T . In this paper we address the question of n