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

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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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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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