Joint Non-parametric Estimation of Mean and Auto-Covariances for Gaussian Processes

Tatyana Krivobokova, Paulo Serra (Corresponding author), Francisco Rosales, Karolina Klockmann

Publications: Contribution to journalArticlePeer Reviewed

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 languageEnglish
Article number107519
Number of pages17
JournalComputational Statistics and Data Analysis
Volume173
Early online date9 May 2022
DOIs
Publication statusPublished - Sep 2022

Austrian Fields of Science 2012

  • 101018 Statistics

Keywords

  • Demmler-Reinsch basis
  • Empirical Bayes
  • Spectral density
  • Stationary process
  • KERNEL REGRESSION
  • CHOICE
  • OPTIMAL RATES
  • MODELS
  • CONVERGENCE
  • BAYESIAN CREDIBLE SETS
  • BANDWIDTH SELECTION

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