Work

Monotone representation and measurability of generalized ψ -estimators

Year: 2026

Type: article

Abstract: We investigate the monotone representation and measurability of generalized ψ-estimators introduced by the authors in 2022. Our first main result, applying the unique existence of a generalized ψ-estimator, allows us to construct this estimator in terms of a function ψ, which is decreasing in its second variable. We then interpret this result as a bridge from a nonconvex optimization problem to a convex one. Further, supposing that the underlying measurable space (sample space) has a measurable diagonal and some additional assumptions on ψ, we show that the measurability of a generalized ψ-estimator is equivalent to the measurability of the corresponding function ψ in its first variable.

Source: Communication in Statistics- Theory and Methods

DOI: 10.1080/03610926.2026.2674120

Authors: Mátyás Barczy, Zsolt Páles

Institutions: University of Szeged, Hungarian Research Network, University of Debrecen

Language: English

Topic: Advanced Statistical Methods and Models

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, Nemzeti Kutatási, Fejlesztési és Innovaciós Alap