Comparison and equality of generalized ψ-estimators

09/09/2023

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by   Matyas Barczy, et al.

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We solve the comparison problem for generalized ψ-estimators introduced in Barczy and Páles (2022). Namely, we derive several necessary and sufficient conditions under which a generalized ψ-estimator less than or equal to another ψ-estimator for any sample. We also solve the corresponding equality problem for generalized ψ-estimators. For applications, we solve the two problems in question for Bajraktarević-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.