Joint non-parametric estimation of mean and auto-covariances for Gaussian processes

Tatyana Krivobokova; Paulo Serra; Francisco Rosales; Karolina Klockmann

doi:10.1016/j.csda.2022.107519

Joint non-parametric estimation of mean and auto-covariances for Gaussian processes

Tatyana Krivobokova, Paulo Serra^*, Francisco Rosales, Karolina Klockmann

^*Corresponding author for this work

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

Gaussian processes that can be decomposed into a smooth mean function and a stationary autocorrelated noise process are considered and a fully automatic nonparametric method to simultaneous estimation of mean and auto-covariance functions of such processes is developed. The proposed empirical Bayes approach is data-driven, numerically efficient, and allows for the construction of confidence sets for the mean function. Performance is demonstrated in simulations and real data analysis. The method is implemented in the R package eBsc.¹

Original language	English
Article number	107519
Pages (from-to)	1-17
Number of pages	17
Journal	Computational Statistics and Data Analysis
Volume	173
Early online date	5 May 2022
DOIs	https://doi.org/10.1016/j.csda.2022.107519
Publication status	Published - Sept 2022

Bibliographical note

Funding Information:
P.S. carried out part of this research while he was a postdoctoral researcher at the Institute of Mathematical Stochastics, Georg-August-Universität Göttingen and would like to acknowledge together with T.K. the support of the German Research Foundation (Deutsche Forschungsgemeinschaft) as part of the Institutional Strategy of the University of Göttingen.

Funding Information:
T.K. would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Statistical Scalability”, where work on this paper was undertaken and supported by EPSRC grant numbers EP/K032208/1 and EP/R014604/1 .

Publisher Copyright:
© 2022 The Author(s)

Funding

P.S. carried out part of this research while he was a postdoctoral researcher at the Institute of Mathematical Stochastics, Georg-August-Universität Göttingen and would like to acknowledge together with T.K. the support of the German Research Foundation (Deutsche Forschungsgemeinschaft) as part of the Institutional Strategy of the University of Göttingen. T.K. would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Statistical Scalability”, where work on this paper was undertaken and supported by EPSRC grant numbers EP/K032208/1 and EP/R014604/1 .

Keywords

Demmler-Reinsch basis
Empirical Bayes
Spectral density
Stationary process

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10.1016/j.csda.2022.107519

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title = "Joint non-parametric estimation of mean and auto-covariances for Gaussian processes",

abstract = "Gaussian processes that can be decomposed into a smooth mean function and a stationary autocorrelated noise process are considered and a fully automatic nonparametric method to simultaneous estimation of mean and auto-covariance functions of such processes is developed. The proposed empirical Bayes approach is data-driven, numerically efficient, and allows for the construction of confidence sets for the mean function. Performance is demonstrated in simulations and real data analysis. The method is implemented in the R package eBsc.1",

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author = "Tatyana Krivobokova and Paulo Serra and Francisco Rosales and Karolina Klockmann",

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AU - Rosales, Francisco

AU - Klockmann, Karolina

N1 - Funding Information: P.S. carried out part of this research while he was a postdoctoral researcher at the Institute of Mathematical Stochastics, Georg-August-Universität Göttingen and would like to acknowledge together with T.K. the support of the German Research Foundation (Deutsche Forschungsgemeinschaft) as part of the Institutional Strategy of the University of Göttingen. Funding Information: T.K. would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Statistical Scalability”, where work on this paper was undertaken and supported by EPSRC grant numbers EP/K032208/1 and EP/R014604/1 . Publisher Copyright: © 2022 The Author(s)

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N2 - Gaussian processes that can be decomposed into a smooth mean function and a stationary autocorrelated noise process are considered and a fully automatic nonparametric method to simultaneous estimation of mean and auto-covariance functions of such processes is developed. The proposed empirical Bayes approach is data-driven, numerically efficient, and allows for the construction of confidence sets for the mean function. Performance is demonstrated in simulations and real data analysis. The method is implemented in the R package eBsc.1

AB - Gaussian processes that can be decomposed into a smooth mean function and a stationary autocorrelated noise process are considered and a fully automatic nonparametric method to simultaneous estimation of mean and auto-covariance functions of such processes is developed. The proposed empirical Bayes approach is data-driven, numerically efficient, and allows for the construction of confidence sets for the mean function. Performance is demonstrated in simulations and real data analysis. The method is implemented in the R package eBsc.1

KW - Demmler-Reinsch basis

KW - Empirical Bayes

KW - Spectral density

KW - Stationary process

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ER -

Joint non-parametric estimation of mean and auto-covariances for Gaussian processes

Abstract

Bibliographical note

Funding

Keywords

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