Adaptive Non-parametric Estimation of Mean and Autocovariance in Regression with Dependent Errors

TL;DR

This paper introduces an automatic, data-driven nonparametric method for jointly estimating the mean and autocovariance functions of Gaussian processes with dependent errors, enabling confidence set construction.

Contribution

It develops a novel empirical Bayes approach for simultaneous estimation of mean and autocovariance functions in dependent error models, with efficient implementation and confidence set capabilities.

Findings

Method performs well in simulations

Effective in real data analysis

Provides confidence sets for mean function

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. Our 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 that accompanies the paper.