Wavelet shrinkage based on the raised cosine prior

Juliana Marchesi Reina; Alex Rodrigo dos Santos Sousa

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arXiv · 2507.10794

Wavelet shrinkage based on the raised cosine prior

Juliana Marchesi Reina·Alex Rodrigo dos Santos Sousa

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Abstract

We propose a Bayesian shrinkage rule to estimate the wavelet coefficients in a nonparametric regression model with Gaussian errors, based on a mixture of a point mass function at zero and a symmetric, zero-centered raised cosine distribution prior. The proposed rule outperformed established shrinkage and thresholding methods in specific scenarios of signal-to-noise ratio and sample size values in conducted simulation studies involving the so-called Donoho and Johnstone test functions. Statistical properties of the rule, such as squared bias, variance, and risks, are analyzed, and two illustrations in real datasets are provided.

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Juliana Marchesi Reina, Alex Rodrigo dos Santos Sousa. 2025-07-14. Wavelet shrinkage based on the raised cosine prior. https://arxiv.org/abs/2507.10794

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