Spatial kernel regression estimation: Weak consistency

Zudi Lu; Xing Chen

doi:10.1016/j.spl.2003.08.014

Spatial kernel regression estimation: Weak consistency

Zudi Lu
, Xing Chen

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

51 Citations (Scopus)

Abstract

In this paper, we introduce a kernel method to estimate a spatial conditional regression under mixing spatial processes. Some preliminary statistical properties including weak consistency and convergence rates are investigated. The sufficient conditions on mixing coefficients and the bandwidth are established to ensure distribution-free weak consistency, which requires no assumption on the regressor and allows the mixing coefficients decreasing to zero slowly. However, to achieve an optimal convergence rate, some requirements on the regressor and the decreasing rate of mixing coefficients tending to zero are needed. © 2003 Published by Elsevier B.V.

Original language	English
Pages (from-to)	125-136
Journal	Statistics and Probability Letters
Volume	68
Issue number	2
DOIs	https://doi.org/10.1016/j.spl.2003.08.014
Publication status	Published - 15 Jun 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 estimator
Mixing spatial processes
Spatial regression
Weak consistency and rates

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title = "Spatial kernel regression estimation: Weak consistency",

abstract = "In this paper, we introduce a kernel method to estimate a spatial conditional regression under mixing spatial processes. Some preliminary statistical properties including weak consistency and convergence rates are investigated. The sufficient conditions on mixing coefficients and the bandwidth are established to ensure distribution-free weak consistency, which requires no assumption on the regressor and allows the mixing coefficients decreasing to zero slowly. However, to achieve an optimal convergence rate, some requirements on the regressor and the decreasing rate of mixing coefficients tending to zero are needed. {\textcopyright} 2003 Published by Elsevier B.V.",

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author = "Zudi Lu and Xing Chen",

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volume = "68",

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TY - JOUR

T1 - Spatial kernel regression estimation

T2 - Weak consistency

AU - Lu, Zudi

AU - Chen, Xing

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].

PY - 2004/6/15

Y1 - 2004/6/15

N2 - In this paper, we introduce a kernel method to estimate a spatial conditional regression under mixing spatial processes. Some preliminary statistical properties including weak consistency and convergence rates are investigated. The sufficient conditions on mixing coefficients and the bandwidth are established to ensure distribution-free weak consistency, which requires no assumption on the regressor and allows the mixing coefficients decreasing to zero slowly. However, to achieve an optimal convergence rate, some requirements on the regressor and the decreasing rate of mixing coefficients tending to zero are needed. © 2003 Published by Elsevier B.V.

AB - In this paper, we introduce a kernel method to estimate a spatial conditional regression under mixing spatial processes. Some preliminary statistical properties including weak consistency and convergence rates are investigated. The sufficient conditions on mixing coefficients and the bandwidth are established to ensure distribution-free weak consistency, which requires no assumption on the regressor and allows the mixing coefficients decreasing to zero slowly. However, to achieve an optimal convergence rate, some requirements on the regressor and the decreasing rate of mixing coefficients tending to zero are needed. © 2003 Published by Elsevier B.V.

KW - Bandwidth

KW - Kernel estimator

KW - Mixing spatial processes

KW - Spatial regression

KW - Weak consistency and rates

UR - https://www.scopus.com/pages/publications/2542435912

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-2542435912&origin=recordpage

U2 - 10.1016/j.spl.2003.08.014

DO - 10.1016/j.spl.2003.08.014

M3 - RGC 21 - Publication in refereed journal

SN - 0167-7152

VL - 68

SP - 125

EP - 136

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -

Spatial kernel regression estimation: Weak consistency

Abstract

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Research Keywords

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