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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2403.17481 |
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| _version_ | 1866911815768735744 |
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| author | Lin, Lu Chen, Ze |
| author_facet | Lin, Lu Chen, Ze |
| contents | The existing Fréchet regression is actually defined within a linear framework, since the weight function in the Fréchet objective function is linearly defined, and the resulting Fréchet regression function is identified to be a linear model when the random object belongs to a Hilbert space. Even for nonparametric and semiparametric Fréchet regressions, which are usually nonlinear, the existing methods handle them by local linear (or local polynomial) technique, and the resulting Fréchet regressions are (locally) linear as well. We in this paper introduce a type of nonlinear Fréchet regressions. Such a framework can be utilized to fit the essentially nonlinear models in a general metric space and uniquely identify the nonlinear structure in a Hilbert space. Particularly, its generalized linear form can return to the standard linear Fréchet regression through a special choice of the weight function. Moreover, the generalized linear form possesses methodological and computational simplicity because the Euclidean variable and the metric space element are completely separable. The favorable theoretical properties (e.g. the estimation consistency and presentation theorem) of the nonlinear Fréchet regressions are established systemically. The comprehensive simulation studies and a human mortality data analysis demonstrate that the new strategy is significantly better than the competitors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17481 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Type of Nonlinear Fréchet Regressions Lin, Lu Chen, Ze Methodology The existing Fréchet regression is actually defined within a linear framework, since the weight function in the Fréchet objective function is linearly defined, and the resulting Fréchet regression function is identified to be a linear model when the random object belongs to a Hilbert space. Even for nonparametric and semiparametric Fréchet regressions, which are usually nonlinear, the existing methods handle them by local linear (or local polynomial) technique, and the resulting Fréchet regressions are (locally) linear as well. We in this paper introduce a type of nonlinear Fréchet regressions. Such a framework can be utilized to fit the essentially nonlinear models in a general metric space and uniquely identify the nonlinear structure in a Hilbert space. Particularly, its generalized linear form can return to the standard linear Fréchet regression through a special choice of the weight function. Moreover, the generalized linear form possesses methodological and computational simplicity because the Euclidean variable and the metric space element are completely separable. The favorable theoretical properties (e.g. the estimation consistency and presentation theorem) of the nonlinear Fréchet regressions are established systemically. The comprehensive simulation studies and a human mortality data analysis demonstrate that the new strategy is significantly better than the competitors. |
| title | A Type of Nonlinear Fréchet Regressions |
| topic | Methodology |
| url | https://arxiv.org/abs/2403.17481 |