Krivobokova, TatyanaSerra, PauloRosales, FranciscoKlockmann, Karolina2023-01-232023-01-232022-05-05Krivobokova, 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.2022.107519https://hdl.handle.net/20.500.12640/3299Gaussian 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.application/pdfenginfo:eu-repo/semantics/openAccessAttribution 4.0 Internationalhttps://creativecommons.org/licenses/by/4.0/Demmler-Reinsch basisEmpirical BayesBase de Demmler-ReinschSpectral densityBayes empíricoDensidad espectralStationary processProceso estacionarioinfo:eu-repo/semantics/articlehttps://doi.org/10.1016/j.csda.2022.107519https://purl.org/pe-repo/ocde/ford#2.11.00