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

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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.1

Suggested Citation

  • Krivobokova, Tatyana & Serra, Paulo & Rosales, Francisco & Klockmann, Karolina, 2022. "Joint non-parametric estimation of mean and auto-covariances for Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:csdana:v:173:y:2022:i:c:s0167947322000998
    DOI: 10.1016/j.csda.2022.107519
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    References listed on IDEAS

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