Moment inequalities for spatial processes

Jiti Gao; Zudi Lu; Dag Tjøstheim

doi:10.1016/j.spl.2007.09.032

Moment inequalities for spatial processes

Jiti Gao
, Zudi Lu
, Dag Tjøstheim

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

9 Citations (Scopus)

Abstract

This paper establishes a general moment inequality for spatial processes satisfying the α-mixing condition [cf., Tran, 1990. Kernel density estimation on random fields. J. Multivariate Analy. 34, 37-53]. Such a general moment inequality is a nontrivial extension of the corresponding result established in Cox and Kim [1995. Moment bounds for mixing random variables useful in nonparametric function estimation. Stochastic Process. Appl. 56, 151-158] for the time series case. As is the case for the Cox-Kim inequality for nonparametric estimation of time series, the new inequality is useful in nonparametric kernel estimation of spatial processes. © 2007 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	687-697
Journal	Statistics and Probability Letters
Volume	78
Issue number	6
DOIs	https://doi.org/10.1016/j.spl.2007.09.032
Publication status	Published - 15 Apr 2008
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

Asymptotic theory
Moment inequality
Nonparametric estimation
Spatial mixing process

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10.1016/j.spl.2007.09.032

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title = "Moment inequalities for spatial processes",

abstract = "This paper establishes a general moment inequality for spatial processes satisfying the α-mixing condition [cf., Tran, 1990. Kernel density estimation on random fields. J. Multivariate Analy. 34, 37-53]. Such a general moment inequality is a nontrivial extension of the corresponding result established in Cox and Kim [1995. Moment bounds for mixing random variables useful in nonparametric function estimation. Stochastic Process. Appl. 56, 151-158] for the time series case. As is the case for the Cox-Kim inequality for nonparametric estimation of time series, the new inequality is useful in nonparametric kernel estimation of spatial processes. {\textcopyright} 2007 Elsevier B.V. All rights reserved.",

keywords = "Asymptotic theory, Moment inequality, Nonparametric estimation, Spatial mixing process",

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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].",

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TY - JOUR

T1 - Moment inequalities for spatial processes

AU - Gao, Jiti

AU - Lu, Zudi

AU - Tjøstheim, Dag

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 - 2008/4/15

Y1 - 2008/4/15

N2 - This paper establishes a general moment inequality for spatial processes satisfying the α-mixing condition [cf., Tran, 1990. Kernel density estimation on random fields. J. Multivariate Analy. 34, 37-53]. Such a general moment inequality is a nontrivial extension of the corresponding result established in Cox and Kim [1995. Moment bounds for mixing random variables useful in nonparametric function estimation. Stochastic Process. Appl. 56, 151-158] for the time series case. As is the case for the Cox-Kim inequality for nonparametric estimation of time series, the new inequality is useful in nonparametric kernel estimation of spatial processes. © 2007 Elsevier B.V. All rights reserved.

AB - This paper establishes a general moment inequality for spatial processes satisfying the α-mixing condition [cf., Tran, 1990. Kernel density estimation on random fields. J. Multivariate Analy. 34, 37-53]. Such a general moment inequality is a nontrivial extension of the corresponding result established in Cox and Kim [1995. Moment bounds for mixing random variables useful in nonparametric function estimation. Stochastic Process. Appl. 56, 151-158] for the time series case. As is the case for the Cox-Kim inequality for nonparametric estimation of time series, the new inequality is useful in nonparametric kernel estimation of spatial processes. © 2007 Elsevier B.V. All rights reserved.

KW - Asymptotic theory

KW - Moment inequality

KW - Nonparametric estimation

KW - Spatial mixing process

UR - https://www.scopus.com/pages/publications/40749148559

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-40749148559&origin=recordpage

U2 - 10.1016/j.spl.2007.09.032

DO - 10.1016/j.spl.2007.09.032

M3 - RGC 21 - Publication in refereed journal

SN - 0167-7152

VL - 78

SP - 687

EP - 697

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 6

ER -

Moment inequalities for spatial processes

Abstract

Bibliographical note

Research Keywords

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