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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.04522 |
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| _version_ | 1866916471575150592 |
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| author | Neumeyer, Natalie Selk, Leonie |
| author_facet | Neumeyer, Natalie Selk, Leonie |
| contents | We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those estimated functions are more challenging in models with infinite-dimensional covariates than in regression models with scalar or vector-valued covariates due to a slower rate of convergence of the parameter estimators. Yet the suggested change point test is asymptotically distribution-free and consistent for one-change point alternatives. In the latter case we also show consistency of a change point estimator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04522 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Testing for changes in the error distribution in functional linear models Neumeyer, Natalie Selk, Leonie Statistics Theory Methodology We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those estimated functions are more challenging in models with infinite-dimensional covariates than in regression models with scalar or vector-valued covariates due to a slower rate of convergence of the parameter estimators. Yet the suggested change point test is asymptotically distribution-free and consistent for one-change point alternatives. In the latter case we also show consistency of a change point estimator. |
| title | Testing for changes in the error distribution in functional linear models |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2411.04522 |