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arXiv · 2511.11067

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

Axel Bücher·Johan Segers·Torben Staud
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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 $-\infty$, hindering the application of existing theorems.

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Axel Bücher, Johan Segers, Torben Staud. 2025-11-14. Consistency of M-estimators for non-identically distributed data: the case of fixed-design distributional regression. https://arxiv.org/abs/2511.11067

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