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

• Autores: Krivobokova, Tatyana, Serra, Paulo, Rosales, Francisco, Klockmann, Karolina
• Formato: artículo
• Fecha de Publicación: 2022
• Institución: Universidad ESAN
• Repositorio: ESAN-Institucional
• Lenguaje: inglés
• OAI Identifier: oai:repositorio.esan.edu.pe:20.500.12640/3299
• Enlace del recurso: https://hdl.handle.net/20.500.12640/3299; https://doi.org/10.1016/j.csda.2022.107519
• Nivel de acceso: acceso abierto
• Materia: Demmler-Reinsch basis; Empirical Bayes; Spectral density; Stationary process; Base de Demmler-Reinsch; Bayes empírico; Densidad espectral; Proceso estacionario; https://purl.org/pe-repo/ocde/ford#2.11.00

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.