Higher-order approximation for uncertainty quantification in time series analysis
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866912388172742656 |
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| author | Betken, Annika Düker, Marie-Christine |
| author_facet | Betken, Annika Düker, Marie-Christine |
| contents | For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a representation as functionals of the empirical process and therefore inherit its slow convergence. As a result, inference based on the asymptotic distribution of those quantities is significantly affected by relatively small sample sizes. We assess the quality of higher-order approximations of the empirical process by deriving the asymptotic distribution of the corresponding error terms. Based on the limiting distribution of the higher-order terms, we propose a novel approach to calculate confidence intervals for statistical quantities such as the median. In a simulation study, we compare coverage rates and lengths of these confidence intervals with those based on the asymptotic distribution of the empirical process and highlight some benefits of higher-order approximations of the empirical process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01108 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Higher-order approximation for uncertainty quantification in time series analysis Betken, Annika Düker, Marie-Christine Statistics Theory For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a representation as functionals of the empirical process and therefore inherit its slow convergence. As a result, inference based on the asymptotic distribution of those quantities is significantly affected by relatively small sample sizes. We assess the quality of higher-order approximations of the empirical process by deriving the asymptotic distribution of the corresponding error terms. Based on the limiting distribution of the higher-order terms, we propose a novel approach to calculate confidence intervals for statistical quantities such as the median. In a simulation study, we compare coverage rates and lengths of these confidence intervals with those based on the asymptotic distribution of the empirical process and highlight some benefits of higher-order approximations of the empirical process. |
| title | Higher-order approximation for uncertainty quantification in time series analysis |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2211.01108 |