Consistency of M-estimators for non-identically distributed data: the case of fixed-design distributional regression
(2025) , 31 pages
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- 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 −∞, hindering the application of existing theorems.
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Citations
Bücher, A., Segers, J., & Staud, T. (2025). Consistency of M-estimators for non-identically distributed data: the case of fixed-design distributional regression (LIDAM Discussion Paper ISBA 2025/21).