We prove that the values of a generalized $\psi$-estimator (introduced by Barczy and P\'ales in 2022) 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 $\psi$-estimators. We also obtain a similar statement for the comparison of generalized $\psi$-estimators using comparative functions, and, as a corollary of this result, we derive the Schweitzer's inequality (also called Kantorovich's inequality).

翻译：我们证明，对于任意长度的样本但仅包含两个不同观测值，广义$\psi$-估计量（由Barczy和Páles于2022年提出）的取值唯一确定了该估计量在任意长度样本（不限制不同观测值的数量）上的取值。换言之，任意长度但仅含两个不同观测值的样本构成了广义$\psi$-估计量的一个确定类。我们还通过比较函数获得了关于广义$\psi$-估计量比较的类似结论，并作为该结果的推论，推导出了Schweitzer不等式（亦称Kantorovich不等式）。