Monotone representation and measurability of generalized $ψ$-estimators
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918486410788864 |
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| author | Barczy, Matyas Páles, Zsolt |
| author_facet | Barczy, Matyas Páles, Zsolt |
| contents | We investigate the monotone representation and measurability of generalized $ψ$-estimators introduced by the authors in 2022. Our first main result, applying the unique existence of a generalized $ψ$-estimator, allows us to construct this estimator in terms of a function $ψ$, which is decreasing in its second variable. We then interpret this result as a bridge from a nonconvex optimization problem to a convex one. Further, supposing that the underlying measurable space (sample space) has a measurable diagonal and some additional assumptions on $ψ$, we show that the measurability of a generalized $ψ$-estimator is equivalent to the measurability of the corresponding function $ψ$ in its first variable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02783 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monotone representation and measurability of generalized $ψ$-estimators Barczy, Matyas Páles, Zsolt Statistics Theory 62F10, 28A05, 26A48, 90C26 We investigate the monotone representation and measurability of generalized $ψ$-estimators introduced by the authors in 2022. Our first main result, applying the unique existence of a generalized $ψ$-estimator, allows us to construct this estimator in terms of a function $ψ$, which is decreasing in its second variable. We then interpret this result as a bridge from a nonconvex optimization problem to a convex one. Further, supposing that the underlying measurable space (sample space) has a measurable diagonal and some additional assumptions on $ψ$, we show that the measurability of a generalized $ψ$-estimator is equivalent to the measurability of the corresponding function $ψ$ in its first variable. |
| title | Monotone representation and measurability of generalized $ψ$-estimators |
| topic | Statistics Theory 62F10, 28A05, 26A48, 90C26 |
| url | https://arxiv.org/abs/2412.02783 |