Comparison and equality of generalized $ψ$-estimators
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908536086200320 |
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| author | Barczy, Matyas Páles, Zsolt |
| author_facet | Barczy, Matyas Páles, Zsolt |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_04773 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Comparison and equality of generalized $ψ$-estimators Barczy, Matyas Páles, Zsolt Statistics Theory 62F10, 62D99, 26E60 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. |
| title | Comparison and equality of generalized $ψ$-estimators |
| topic | Statistics Theory 62F10, 62D99, 26E60 |
| url | https://arxiv.org/abs/2309.04773 |