Year: 2024
Type: preprint
Abstract: We prove that the values of a generalized $ψ$-estimator (introduced by Barczy and Páles in 2025) on samples of arbitrary length but having only two different observations uniquely determine the values of the estimator on any sample of arbitrary length without any restriction on the number of different observations. In other words, samples of arbitrary length but having only two different observations form a determining class for generalized $ψ$-estimators. We also obtain a similar statement for the comparison of generalized $ψ$-estimators using comparative functions, and, as a corollary of this result, we derive the Schweitzer's inequality (also called Kantorovich's inequality).
Source: arXiv (Cornell University)
Authors: Barczy, Matyas, Páles, Zsolt
Institutions: University of Debrecen, University of Szeged
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4391948980