Determining classes for generalized $ψ$-estimators
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914190298447872 |
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| author | Barczy, Matyas Páles, Zsolt |
| author_facet | Barczy, Matyas Páles, Zsolt |
| contents | We prove that the values of a generalized $ψ$-estimator (introduced by Barczy and Páles in 2025) on samples of arbitrary length but having only two different observations uniquely determine the values of the estimator on any sample of arbitrary length without any restriction on the number of different observations. In other words, samples of arbitrary length but having only two different observations form a determining class for generalized $ψ$-estimators. We also obtain a similar statement for the comparison of generalized $ψ$-estimators using comparative functions, and, as a corollary of this result, we derive the Schweitzer's inequality (also called Kantorovich's inequality). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10817 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Determining classes for generalized $ψ$-estimators Barczy, Matyas Páles, Zsolt Statistics Theory Classical Analysis and ODEs 62F10, 26E60, 26D15 We prove that the values of a generalized $ψ$-estimator (introduced by Barczy and Páles in 2025) on samples of arbitrary length but having only two different observations uniquely determine the values of the estimator on any sample of arbitrary length without any restriction on the number of different observations. In other words, samples of arbitrary length but having only two different observations form a determining class for generalized $ψ$-estimators. We also obtain a similar statement for the comparison of generalized $ψ$-estimators using comparative functions, and, as a corollary of this result, we derive the Schweitzer's inequality (also called Kantorovich's inequality). |
| title | Determining classes for generalized $ψ$-estimators |
| topic | Statistics Theory Classical Analysis and ODEs 62F10, 26E60, 26D15 |
| url | https://arxiv.org/abs/2402.10817 |