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

2025/11/14 by Axel Bücher, Johan Segers, Bücher, Axel +3
Economics, Econometrics and Finance · Mathematics · #62F10 #62F12 (Primary) #62G32 (Secondary) #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2511.11067

openalex publication_date 2025/11/14 · openalex created_date 2025/11/18 · openalex updated_date 2026/07/28

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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