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

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https://www.sciencedirect.com/science/article/pii/S0167947322000998/pdfft?md5=b4009fe50e464f6c2c4717b7b42e1541&pid=1-s2.0-S0167947322000998-main.pdf
Date
2022-05-05
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Elsevier
International Association for Statistical Computing
Computational and Methodological Statistics
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Krivobokova, Tatyana ; Serra, Paulo ; Rosales, Francisco ; Klockmann, Karolina
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.
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Keywords
Demmler-Reinsch basis, Empirical Bayes, Base de Demmler-Reinsch, Spectral density, Bayes empírico, Densidad espectral, Stationary process, Proceso estacionario
Citation
Krivobokova, T., Serra, P., Rosales, F., & Klockmann, K. (2022). Joint non-parametric estimation of mean and auto-covariances for Gaussian processes. Computational Statistics and Data Analysis, 173(2022), 107519. https://doi.org/10.1016/j.csda.2022.107519
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https://hdl.handle.net/20.500.12640/3299
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