Adaptive thresholding for wavelet-based nonparametric heteroskedastic variance estimation on the sphere
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915713958019072 |
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| author | Durastanti, Claudio Shevchenko, Radomyra |
| author_facet | Durastanti, Claudio Shevchenko, Radomyra |
| contents | This paper investigates the nonparametric estimation of a heteroskedastic variance function on the sphere in a regression framework, assuming the variance belongs to a Besov regularity class. A needlet-based estimator is proposed, combining multiresolution analysis with hard thresholding. The method exploits the spatial and spectral localization of needlets to adapt to unknown smoothness and is shown to attain minimax-optimal convergence rates over Besov spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_03920 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive thresholding for wavelet-based nonparametric heteroskedastic variance estimation on the sphere Durastanti, Claudio Shevchenko, Radomyra Statistics Theory 62G08, 62G20, 65T60 This paper investigates the nonparametric estimation of a heteroskedastic variance function on the sphere in a regression framework, assuming the variance belongs to a Besov regularity class. A needlet-based estimator is proposed, combining multiresolution analysis with hard thresholding. The method exploits the spatial and spectral localization of needlets to adapt to unknown smoothness and is shown to attain minimax-optimal convergence rates over Besov spaces. |
| title | Adaptive thresholding for wavelet-based nonparametric heteroskedastic variance estimation on the sphere |
| topic | Statistics Theory 62G08, 62G20, 65T60 |
| url | https://arxiv.org/abs/2601.03920 |