ON FIXED-DOMAIN ASYMPTOTICS, PARAMETER ESTIMATION and ISOTROPIC GAUSSIAN RANDOM FIELDS with MATÉRN COVARIANCE FUNCTIONS

Wei-Liem Loh; Saifei Sun; Jun Wen

doi:10.1214/21-AOS2077

ON FIXED-DOMAIN ASYMPTOTICS, PARAMETER ESTIMATION and ISOTROPIC GAUSSIAN RANDOM FIELDS with MATÉRN COVARIANCE FUNCTIONS

Wei-Liem Loh^*
, Saifei Sun
, Jun Wen

^*Corresponding author for this work

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

17 Citations (Scopus)

Abstract

A method is proposed for estimating the microergodic parameters (including the smoothness parameter) of stationary Gaussian random fields on ℝ^d with isotropic Matérn covariance functions using irregularly spaced data. This approach uses higher-order quadratic variations and is applied to three designs, namely stratified sampling design, randomized sampling design and deformed lattice design. Microergodic parameter estimators are constructed for each of the designs. Under mild conditions, these estimators are shown to be consistent with respect to fixed-domain asymptotics. Upper bounds to the convergence rate of the estimators are also established. A simulation study is conducted to gauge the accuracy of the proposed estimators. © Institute of Mathematical Statistics, 2021

Original language	English
Pages (from-to)	3127-3152
Journal	Annals of Statistics
Volume	49
Issue number	6
DOIs	https://doi.org/10.1214/21-AOS2077
Publication status	Published - Dec 2021
Externally published	Yes

Funding

The first author was supported by AcRF Tier 1 Grant R-155-000-209-114.

Research Keywords

Consistency
Convergence rate
Deformed lattice
Fixed-domain asymptotics
Gaussian random field
Irregularly spaced data
Matérn covariance
Microergodic parameter
Quadratic variation
Random sampling
Smoothness

Access Output

10.1214/21-AOS2077

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{7ddadf5e46ad4bd692c12ebf19aef24e,

title = "ON FIXED-DOMAIN ASYMPTOTICS, PARAMETER ESTIMATION and ISOTROPIC GAUSSIAN RANDOM FIELDS with MAT{\'E}RN COVARIANCE FUNCTIONS",

abstract = "A method is proposed for estimating the microergodic parameters (including the smoothness parameter) of stationary Gaussian random fields on ℝd with isotropic Mat{\'e}rn covariance functions using irregularly spaced data. This approach uses higher-order quadratic variations and is applied to three designs, namely stratified sampling design, randomized sampling design and deformed lattice design. Microergodic parameter estimators are constructed for each of the designs. Under mild conditions, these estimators are shown to be consistent with respect to fixed-domain asymptotics. Upper bounds to the convergence rate of the estimators are also established. A simulation study is conducted to gauge the accuracy of the proposed estimators. {\textcopyright} Institute of Mathematical Statistics, 2021",

keywords = "Consistency, Convergence rate, Deformed lattice, Fixed-domain asymptotics, Gaussian random field, Irregularly spaced data, Mat{\'e}rn covariance, Microergodic parameter, Quadratic variation, Random sampling, Smoothness",

author = "Wei-Liem Loh and Saifei Sun and Jun Wen",

year = "2021",

month = dec,

doi = "10.1214/21-AOS2077",

language = "English",

volume = "49",

pages = "3127--3152",

journal = "Annals of Statistics",

issn = "0090-5364",

publisher = "Institute of Mathematical Statistics",

number = "6",

}

TY - JOUR

T1 - ON FIXED-DOMAIN ASYMPTOTICS, PARAMETER ESTIMATION and ISOTROPIC GAUSSIAN RANDOM FIELDS with MATÉRN COVARIANCE FUNCTIONS

AU - Loh, Wei-Liem

AU - Sun, Saifei

AU - Wen, Jun

PY - 2021/12

Y1 - 2021/12

N2 - A method is proposed for estimating the microergodic parameters (including the smoothness parameter) of stationary Gaussian random fields on ℝd with isotropic Matérn covariance functions using irregularly spaced data. This approach uses higher-order quadratic variations and is applied to three designs, namely stratified sampling design, randomized sampling design and deformed lattice design. Microergodic parameter estimators are constructed for each of the designs. Under mild conditions, these estimators are shown to be consistent with respect to fixed-domain asymptotics. Upper bounds to the convergence rate of the estimators are also established. A simulation study is conducted to gauge the accuracy of the proposed estimators. © Institute of Mathematical Statistics, 2021

AB - A method is proposed for estimating the microergodic parameters (including the smoothness parameter) of stationary Gaussian random fields on ℝd with isotropic Matérn covariance functions using irregularly spaced data. This approach uses higher-order quadratic variations and is applied to three designs, namely stratified sampling design, randomized sampling design and deformed lattice design. Microergodic parameter estimators are constructed for each of the designs. Under mild conditions, these estimators are shown to be consistent with respect to fixed-domain asymptotics. Upper bounds to the convergence rate of the estimators are also established. A simulation study is conducted to gauge the accuracy of the proposed estimators. © Institute of Mathematical Statistics, 2021

KW - Consistency

KW - Convergence rate

KW - Deformed lattice

KW - Fixed-domain asymptotics

KW - Gaussian random field

KW - Irregularly spaced data

KW - Matérn covariance

KW - Microergodic parameter

KW - Quadratic variation

KW - Random sampling

KW - Smoothness

UR - https://www.scopus.com/pages/publications/85122197239

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85122197239&origin=recordpage

U2 - 10.1214/21-AOS2077

DO - 10.1214/21-AOS2077

M3 - RGC 21 - Publication in refereed journal

SN - 0090-5364

VL - 49

SP - 3127

EP - 3152

JO - Annals of Statistics

JF - Annals of Statistics

IS - 6

ER -

ON FIXED-DOMAIN ASYMPTOTICS, PARAMETER ESTIMATION and ISOTROPIC GAUSSIAN RANDOM FIELDS with MATÉRN COVARIANCE FUNCTIONS

Abstract

Funding

Research Keywords

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Cite this