{"ID":2841587,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.11067","arxiv_id":"2511.11067","title":"Consistency of M-estimators for non-identically distributed data: the case of fixed-design distributional regression","abstract":"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.","short_abstract":"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 s...","url_abs":"https://arxiv.org/abs/2511.11067","url_pdf":"https://arxiv.org/pdf/2511.11067v1","authors":"[\"Axel Bücher\",\"Johan Segers\",\"Torben Staud\"]","published":"2025-11-14T08:35:29Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}