Nonparametric testing for the specification of spatial trend functions

Rongmao Zhang; Ngai Hang Chan; Changxiong Chi

doi:10.1016/j.jmva.2023.105180

Nonparametric testing for the specification of spatial trend functions

Rongmao Zhang^*, Ngai Hang Chan, Changxiong Chi

^*Corresponding author for this work

Department of Biostatistics

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

1 Citation (Scopus)

Abstract

Correct specification of a spatial trend constitutes an important topic in statistics because it facilitates spatial kriging and inference. This paper proposes a global integrated squared error (GISE) statistics between the nonparametric smoothing surface and the parametric hypothesized model to test for the goodness-of-fit of spatial trends. By virtue of the m-dependence approximation of a stationary random field, it is shown that under certain regularity conditions, the proposed GISE statistics has an asymptotic normal distribution. Further, a grid-based block bootstrap (GBBB) procedure is also proposed to deal with the complicated asymptotic variance involved in the limit distribution. Numerical studies are also presented to illustrate the performance of the proposed method. © 2023 Elsevier Inc.

Original language	English
Article number	105180
Journal	Journal of Multivariate Analysis
Volume	196
Online published	18 Mar 2023
DOIs	https://doi.org/10.1016/j.jmva.2023.105180
Publication status	Published - Jul 2023

Bibliographical note

Full text of this publication does not contain sufficient affiliation information. With consent from the author(s) concerned, the Research Unit(s) information for this record is based on the existing academic department affiliation of the author(s).

Funding

We would like to thank the Editor, an Associate Editor, and two anonymous referees for their critical comments and thoughtful suggestions, which led to a much improved version of this paper. This research was supported in part by grants from NSFC, China (Nos. 12171427, 11771390, U21A20426), Zhejiang provincial natural science foundation (No. LZ21A010002), and HKSAR-RGC-GRF, China Nos. 14325216, 14307921 (Chan).

Research Keywords

Goodness-of-fit
Grid-based block bootstrap
m-dependence approximation
Nonparametric smoothing
Spatial trends

RGC Funding Information

RGC-funded

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@article{20317f09a9654a368ae1770d6043d7d6,

title = "Nonparametric testing for the specification of spatial trend functions",

abstract = "Correct specification of a spatial trend constitutes an important topic in statistics because it facilitates spatial kriging and inference. This paper proposes a global integrated squared error (GISE) statistics between the nonparametric smoothing surface and the parametric hypothesized model to test for the goodness-of-fit of spatial trends. By virtue of the m-dependence approximation of a stationary random field, it is shown that under certain regularity conditions, the proposed GISE statistics has an asymptotic normal distribution. Further, a grid-based block bootstrap (GBBB) procedure is also proposed to deal with the complicated asymptotic variance involved in the limit distribution. Numerical studies are also presented to illustrate the performance of the proposed method. {\textcopyright} 2023 Elsevier Inc.",

keywords = "Goodness-of-fit, Grid-based block bootstrap, m-dependence approximation, Nonparametric smoothing, Spatial trends",

author = "Rongmao Zhang and Chan, {Ngai Hang} and Changxiong Chi",

note = "Full text of this publication does not contain sufficient affiliation information. With consent from the author(s) concerned, the Research Unit(s) information for this record is based on the existing academic department affiliation of the author(s).",

year = "2023",

month = jul,

doi = "10.1016/j.jmva.2023.105180",

language = "English",

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journal = "Journal of Multivariate Analysis",

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T1 - Nonparametric testing for the specification of spatial trend functions

AU - Zhang, Rongmao

AU - Chan, Ngai Hang

AU - Chi, Changxiong

N1 - Full text of this publication does not contain sufficient affiliation information. With consent from the author(s) concerned, the Research Unit(s) information for this record is based on the existing academic department affiliation of the author(s).

PY - 2023/7

Y1 - 2023/7

N2 - Correct specification of a spatial trend constitutes an important topic in statistics because it facilitates spatial kriging and inference. This paper proposes a global integrated squared error (GISE) statistics between the nonparametric smoothing surface and the parametric hypothesized model to test for the goodness-of-fit of spatial trends. By virtue of the m-dependence approximation of a stationary random field, it is shown that under certain regularity conditions, the proposed GISE statistics has an asymptotic normal distribution. Further, a grid-based block bootstrap (GBBB) procedure is also proposed to deal with the complicated asymptotic variance involved in the limit distribution. Numerical studies are also presented to illustrate the performance of the proposed method. © 2023 Elsevier Inc.

AB - Correct specification of a spatial trend constitutes an important topic in statistics because it facilitates spatial kriging and inference. This paper proposes a global integrated squared error (GISE) statistics between the nonparametric smoothing surface and the parametric hypothesized model to test for the goodness-of-fit of spatial trends. By virtue of the m-dependence approximation of a stationary random field, it is shown that under certain regularity conditions, the proposed GISE statistics has an asymptotic normal distribution. Further, a grid-based block bootstrap (GBBB) procedure is also proposed to deal with the complicated asymptotic variance involved in the limit distribution. Numerical studies are also presented to illustrate the performance of the proposed method. © 2023 Elsevier Inc.

KW - Goodness-of-fit

KW - Grid-based block bootstrap

KW - m-dependence approximation

KW - Nonparametric smoothing

KW - Spatial trends

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U2 - 10.1016/j.jmva.2023.105180

DO - 10.1016/j.jmva.2023.105180

M3 - RGC 21 - Publication in refereed journal

SN - 0047-259X

VL - 196

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

M1 - 105180

ER -

Nonparametric testing for the specification of spatial trend functions

Abstract

Bibliographical note

Funding

Research Keywords

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GRF: Statistical Modeling of Big Data Networks

Cite this

Nonparametric testing for the specification of spatial trend functions

Abstract

Bibliographical note

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

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GRF: Statistical Modeling of Big Data Networks

Cite this