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Comparison and equality of generalized $ψ$-estimators
Matyas Barczy, Zsolt Páles · 2023-09-09 · via math.ST updates on arXiv.org

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 solutions of likelihood equations in case of normal, a Beta-type, Gamma, Lomax (Pareto type II), lognormal and Laplace distributions.

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