We establish several properties of (weighted) generalized $\psi$-estimators introduced by Barczy and P\'ales in 2022: mean-type, monotonicity and sensitivity properties, bisymmetry-type inequality and some asymptotic and continuity properties as well. We also illustrate these properties by providing several examples including statistical ones as well.

翻译：我们研究了Barczy和Páles于2022年提出的（加权）广义$ψ$-估计量的若干性质：均值型性质、单调性和敏感性性质、双对称型不等式，以及一些渐近和连续性性质。我们还通过提供若干示例（包括统计示例）来说明这些性质。