On Bayesian wavelet shrinkage estimation of nonparametric regression models with stationary errors

TL;DR

This paper introduces a Bayesian wavelet shrinkage method for nonparametric regression with stationary errors, demonstrating its effectiveness over standard methods through simulations and real data analysis.

Contribution

It proposes a novel Bayesian rule combining a point mass at zero and a logistic distribution for wavelet shrinkage in models with correlated errors.

Findings

Performance remains stable with increasing error correlation.

Outperforms standard soft thresholding in most scenarios.

Maintains accuracy across different sample sizes and signal-to-noise ratios.

Abstract

This work proposes a Bayesian rule based on the mixture of a point mass function at zero and the logistic distribution to perform wavelet shrinkage in nonparametric regression models with stationary errors (with short or long-memory behavior). The proposal is assessed through Monte Carlo experiments and illustrated with real data. Simulation studies indicate that the precision of the estimates decreases as the amount of correlation increases. However, given a sample size and error correlated noise, the performance of the rule is almost the same while the signal-to-noise ratio decreases, compared to the performance of the rule under independent and identically distributed errors. Further, we find that the performance of the proposal is better than the standard soft thresholding rule with universal policy in most of the considered underlying functions, sample sizes and signal-to-noise ratios scenarios.