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arXiv · 2412.02783

Monotone representation and measurability of generalized $\psi$-estimators

Matyas Barczy·Zsolt Páles
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Abstract

We investigate the monotone representation and measurability of generalized $\psi$-estimators introduced by the authors in 2022. Our first main result, applying the unique existence of a generalized $\psi$-estimator, allows us to construct this estimator in terms of a function $\psi$, 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 $\psi$, we show that the measurability of a generalized $\psi$-estimator is equivalent to the measurability of the corresponding function $\psi$ in its first variable.

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Matyas Barczy, Zsolt Páles. 2024-12-03. Monotone representation and measurability of generalized $\psi$-estimators. https://arxiv.org/abs/2412.02783

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