Consistency of M-estimators for non-identically distributed data: the case of fixed-design distributional regression
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915618053160960 |
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| author | Bücher, Axel Segers, Johan Staud, Torben |
| author_facet | Bücher, Axel Segers, Johan Staud, Torben |
| contents | This paper explores strong and weak consistency of M-estimators for non-identically distributed data, extending prior work. Emphasis is given to scenarios where data is viewed as a triangular array, which encompasses distributional regression models with non-random covariates. Primitive conditions are established for specific applications, such as estimation based on minimizing empirical proper scoring rules or conditional maximum likelihood. A key motivation is addressing challenges in extreme value statistics, where parameter-dependent supports can cause criterion functions to attain the value $-\infty$, hindering the application of existing theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11067 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Consistency of M-estimators for non-identically distributed data: the case of fixed-design distributional regression Bücher, Axel Segers, Johan Staud, Torben Statistics Theory 62F10, 62F12 (Primary), 62G32 (Secondary) This paper explores strong and weak consistency of M-estimators for non-identically distributed data, extending prior work. Emphasis is given to scenarios where data is viewed as a triangular array, which encompasses distributional regression models with non-random covariates. Primitive conditions are established for specific applications, such as estimation based on minimizing empirical proper scoring rules or conditional maximum likelihood. A key motivation is addressing challenges in extreme value statistics, where parameter-dependent supports can cause criterion functions to attain the value $-\infty$, hindering the application of existing theorems. |
| title | Consistency of M-estimators for non-identically distributed data: the case of fixed-design distributional regression |
| topic | Statistics Theory 62F10, 62F12 (Primary), 62G32 (Secondary) |
| url | https://arxiv.org/abs/2511.11067 |