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

Author

Listed:
  • Mátyás Barczy

    (Bolyai Institute, University of Szeged)

  • Zsolt Páles

    (University of Debrecen)

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.

Suggested Citation

  • Mátyás Barczy & Zsolt Páles, 2025. "Comparison and equality of generalized $$\psi $$ ψ -estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(2), pages 217-250, April.
    • Handle: RePEc:spr:aistmt:v:77:y:2025:i:2:d:10.1007_s10463-024-00916-7
    DOI: 10.1007/s10463-024-00916-7
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    References listed on IDEAS

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    1. Tian, Yongge & Wiens, Douglas P., 2006. "On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1265-1272, July.
    2. Bo Jiang & Yuqin Sun, 2019. "On the equality of estimators under a general partitioned linear model with parameter restrictions," Statistical Papers, Springer, vol. 60(1), pages 273-292, February.
    3. Lu, Cuicui & Schmidt, Peter, 2012. "Conditions for the numerical equality of the OLS, GLS and Amemiya–Cragg estimators," Economics Letters, Elsevier, vol. 116(3), pages 538-540.
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