Wavelet shrinkage based on the raised cosine prior
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916843837456384 |
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| author | Reina, Juliana Marchesi Sousa, Alex Rodrigo dos Santos |
| author_facet | Reina, Juliana Marchesi Sousa, Alex Rodrigo dos Santos |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10794 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wavelet shrinkage based on the raised cosine prior Reina, Juliana Marchesi Sousa, Alex Rodrigo dos Santos Methodology 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. |
| title | Wavelet shrinkage based on the raised cosine prior |
| topic | Methodology |
| url | https://arxiv.org/abs/2507.10794 |