The Annals of Statistics

Some asymptotic results of Gaussian random fields with varying mean functions and the associated processes

Jingchen Liu and Gongjun Xu

Full-text: Open access

Abstract

In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple applications such as hypothesis testing for spatial models and financial applications.

Article information

Source
Ann. Statist., Volume 40, Number 1 (2012), 262-293.

Dates
First available in Project Euclid: 29 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.aos/1333029965

Digital Object Identifier
doi:10.1214/11-AOS960

Mathematical Reviews number (MathSciNet)
MR3014307

Zentralblatt MATH identifier
1246.60056

Subjects
Primary: 60G15: Gaussian processes 65C05: Monte Carlo methods

Keywords
Gaussian process integral change of measure

Citation

Liu, Jingchen; Xu, Gongjun. Some asymptotic results of Gaussian random fields with varying mean functions and the associated processes. Ann. Statist. 40 (2012), no. 1, 262--293. doi:10.1214/11-AOS960. https://projecteuclid.org/euclid.aos/1333029965


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Supplemental materials

  • Supplementary material: Proofs of several lemmas in Section 5 and the numerical results. This supplement contains proofs of Lemmas 5.2, 5.4, 5.5, 5.8 and 5.9 as well as numerical results.