Distributional hyperspace-convergence of Argmin-sets in convex -estimation

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

In M-estimation we consider the sets of all minimizing points of convex empirical criterion functions. These sets are random closed sets. We derive distributional convergence in the hyperspace of all closed subsets of the real line endowed with the Fell-topology. As a special case single minimizing points converge in distribution in the classical sense. In contrast to the literature so far, unusual rates of convergence and non-normal limits emerge, which go far beyond the square-root asymptotic normality. Moreover, our theory can be applied to the sets of zero-estimators.

Details

OriginalspracheEnglisch
Seiten (von - bis)3-25
Seitenumfang22
FachzeitschriftTheory of probability and mathematical statistics
Jahrgang109
Frühes Online-DatumOkt. 2023
PublikationsstatusVeröffentlicht - 2023
Peer-Review-StatusJa

Externe IDs

WOS 001084577300001
Scopus 85163988294

Schlagworte

Schlagwörter

  • Argmin-sets, Fell-topology, M-estimation, Convex empirical processes, Random closed sets

Bibliotheksschlagworte