Comparison and equality of generalized $$\psi $$ ψ -estimators

Mátyás Barczy () and Zsolt Páles ()
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Mátyás Barczy: Bolyai Institute, University of Szeged
Zsolt Páles: University of Debrecen

Annals of the Institute of Statistical Mathematics, 2025, vol. 77, issue 2, No 2, 217-250

Abstract: Abstract We solve the comparison problem for generalized $$\psi $$ ψ -estimators introduced by Barczy and Páles (arXiv: 2211.06026, 2022). Namely, we derive several necessary and sufficient conditions under which a generalized $$\psi $$ ψ -estimator less than or equal to another $$\psi $$ ψ -estimator for any sample. We also solve the corresponding equality problem for generalized $$\psi $$ ψ -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.

Keywords: $$\psi $$ ψ -estimator; Z-estimator; Comparison of estimators; Equality of estimators; Likelihood equation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10463-024-00916-7

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