Compositional Periodic Spline Approximation for Circular Density Data in Bayes Spaces
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917508074700800 |
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| author | Machalová, Jitka Heckenbergerová, Jana Hron, Karel |
| author_facet | Machalová, Jitka Heckenbergerová, Jana Hron, Karel |
| contents | This paper proposes a novel framework for the approximation and analysis of circular density data using compositional periodic splines within Bayes spaces with the Hilbert space structure. By applying the centered log-ratio transformation, densities are represented in a subspace of the standard $L^2$ space of real-valued functions, which enables the use of functional data analysis tools while preserving the relative nature of distributions and their periodic structure. A coefficient-based construction of periodic splines with a zero-integral constraint is developed, together with matrix formulations for both smoothing splines and penalized splines, allowing efficient estimation and implementation. The methodology is applied to long-term wind direction data, where it provides smooth and interpretable density estimates and supports further statistical analysis, including functional regression. The results demonstrate the practical relevance of the proposed approach and its potential for extensions to more complex density-valued data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18339 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Compositional Periodic Spline Approximation for Circular Density Data in Bayes Spaces Machalová, Jitka Heckenbergerová, Jana Hron, Karel Methodology Statistics Theory This paper proposes a novel framework for the approximation and analysis of circular density data using compositional periodic splines within Bayes spaces with the Hilbert space structure. By applying the centered log-ratio transformation, densities are represented in a subspace of the standard $L^2$ space of real-valued functions, which enables the use of functional data analysis tools while preserving the relative nature of distributions and their periodic structure. A coefficient-based construction of periodic splines with a zero-integral constraint is developed, together with matrix formulations for both smoothing splines and penalized splines, allowing efficient estimation and implementation. The methodology is applied to long-term wind direction data, where it provides smooth and interpretable density estimates and supports further statistical analysis, including functional regression. The results demonstrate the practical relevance of the proposed approach and its potential for extensions to more complex density-valued data. |
| title | Compositional Periodic Spline Approximation for Circular Density Data in Bayes Spaces |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2605.18339 |