Fast nonparametric spectral density estimation from irregularly sampled data
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911191464411136 |
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| author | Geoga, Christopher J. Beckman, Paul G. |
| author_facet | Geoga, Christopher J. Beckman, Paul G. |
| contents | We introduce a nonparametric spectral density estimator for continuous-time and continuous-space processes measured at fully irregular locations. Our estimator is constructed using a weighted nonuniform Fourier sum whose weights yield a high-accuracy quadrature rule with respect to a user-specified window function. The resulting estimator significantly reduces the aliasing seen in periodogram approaches and least squares spectral analysis, sidesteps the dangers of ill-conditioning of the nonuniform Fourier inverse problem, and can be adapted to a wide variety of irregular sampling settings. We describe methods for rapidly computing the necessary weights in various settings, making the estimator scalable to large datasets. We then provide a theoretical analysis of sources of bias, and close with demonstrations of the method's efficacy, including for processes that exhibit very slow spectral decay and are observed at up to a million locations in multiple dimensions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_00492 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast nonparametric spectral density estimation from irregularly sampled data Geoga, Christopher J. Beckman, Paul G. Methodology Numerical Analysis We introduce a nonparametric spectral density estimator for continuous-time and continuous-space processes measured at fully irregular locations. Our estimator is constructed using a weighted nonuniform Fourier sum whose weights yield a high-accuracy quadrature rule with respect to a user-specified window function. The resulting estimator significantly reduces the aliasing seen in periodogram approaches and least squares spectral analysis, sidesteps the dangers of ill-conditioning of the nonuniform Fourier inverse problem, and can be adapted to a wide variety of irregular sampling settings. We describe methods for rapidly computing the necessary weights in various settings, making the estimator scalable to large datasets. We then provide a theoretical analysis of sources of bias, and close with demonstrations of the method's efficacy, including for processes that exhibit very slow spectral decay and are observed at up to a million locations in multiple dimensions. |
| title | Fast nonparametric spectral density estimation from irregularly sampled data |
| topic | Methodology Numerical Analysis |
| url | https://arxiv.org/abs/2503.00492 |