We solve the comparison problem for generalized $\psi$-estimators introduced in Barczy and P\'ales (2022). Namely, we derive several necessary and sufficient conditions under which a generalized $\psi$-estimator less than or equal to another $\psi$-estimator for any sample. We also solve the corresponding equality problem for generalized $\psi$-estimators. For applications, we solve the two problems in question for Bajraktarevi\'c-type- and quasi-arithmetic-type estimators. We also apply our results for some known statistical estimators such as for empirical expectiles and Mathieu-type estimators and for solving likelihood equations in case of normal, a Beta-type, Gamma, Lomax (Pareto type II), lognormal and Laplace distributions.

翻译：我们解决了Barczy与Páles（2022）提出的广义ψ-估计量的比较问题。具体而言，我们推导出若干充要条件，使得对于任意样本，一个广义ψ-估计量小于或等于另一个ψ-估计量。同时，我们还解决了广义ψ-估计量的相应相等性问题。在应用方面，我们针对Bajraktarević型估计量和拟算术型估计量解决了这两个问题。此外，我们将所得结果应用于若干已知统计估计量，如经验期望分位数和Mathieu型估计量，并用于求解正态分布、Beta型分布、伽马分布、洛马克斯分布（帕累托Ⅱ型）、对数正态分布及拉普拉斯分布下的似然方程。