Consistency of M-estimators for non-identically distributed data: the case of fixed-design distributional regression

Axel Bücher, Johan Segers () and Torben Staud
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Johan Segers: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2025021, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

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.

Keywords: Block-Maxima Method; Conditional Maximum Likelihood; Distributional Regression; Minimum Scoring Rule Estimation; Non-Random Covariates (search for similar items in EconPapers)
Pages: 31
Date: 2025-11-17
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