Density-valued time series: Nonparametric density-on-density regression
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917006032240640 |
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| author | Ferraty, Frédéric Shang, Han Lin |
| author_facet | Ferraty, Frédéric Shang, Han Lin |
| contents | This paper is concerned with forecasting probability density functions. Density functions are nonnegative and have a constrained integral; thus, they do not constitute a vector space. Implementing unconstrained functional time-series forecasting methods is problematic for such nonlinear and constrained data. A novel forecasting method is developed based on a nonparametric function-on-function regression, where both the response and the predictor are probability density functions. Asymptotic properties of our nonparametric regression estimator are established, as well as its finite-sample performance through a series of Monte-Carlo simulation studies. Using COVID-19 data from the French department and age-specific period life tables from the United States, we assess and compare the finite-sample forecast accuracy of the proposed method with several existing methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22904 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Density-valued time series: Nonparametric density-on-density regression Ferraty, Frédéric Shang, Han Lin Methodology Applications 62R10, 62P25 This paper is concerned with forecasting probability density functions. Density functions are nonnegative and have a constrained integral; thus, they do not constitute a vector space. Implementing unconstrained functional time-series forecasting methods is problematic for such nonlinear and constrained data. A novel forecasting method is developed based on a nonparametric function-on-function regression, where both the response and the predictor are probability density functions. Asymptotic properties of our nonparametric regression estimator are established, as well as its finite-sample performance through a series of Monte-Carlo simulation studies. Using COVID-19 data from the French department and age-specific period life tables from the United States, we assess and compare the finite-sample forecast accuracy of the proposed method with several existing methods. |
| title | Density-valued time series: Nonparametric density-on-density regression |
| topic | Methodology Applications 62R10, 62P25 |
| url | https://arxiv.org/abs/2503.22904 |