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

Author

Listed:
  • Bücher, Axel
  • Segers, Johan

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Staud, Torben

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.

Suggested Citation

  • Bücher, Axel & Segers, Johan & Staud, Torben, 2025. "Consistency of M-estimators for non-identically distributed data: the case of fixed-design distributional regression," LIDAM Discussion Papers ISBA 2025021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2025021
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