Kernel Debiased Plug-in Estimation based on the Universal Least Favorable Submodel
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917327833923584 |
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| author | Chen, Haiyi Liu, Yang Malenica, Ivana |
| author_facet | Chen, Haiyi Liu, Yang Malenica, Ivana |
| contents | We propose ULFS-KDPE, a kernel debiased plug-in estimator based on the universal least favorable submodel, for estimating pathwise differentiable parameters in nonparametric models. The method constructs a data-adaptive debiasing flow in a reproducing kernel Hilbert space (RKHS), producing a plug-in estimator that achieves semiparametric efficiency without requiring explicit derivation or evaluation of efficient influence functions. We place ULFS-KDPE on a rigorous functional-analytic foundation by formulating the universal least favorable update as a nonlinear ordinary differential equation on probability densities. We establish existence, uniqueness, stability, and finite-time convergence of the empirical score along the induced flow. Under standard regularity conditions, the resulting estimator is regular, asymptotically linear, and attains the semiparametric efficiency bound simultaneously for a broad class of pathwise differentiable parameters. The method admits a computationally tractable implementation based on finite-dimensional kernel representations and principled stopping criteria. In finite samples, the combination of solving a rich collection of score equations with RKHS-based smoothing and avoidance of direct influence-function evaluation leads to improved numerical stability. Simulation studies illustrate the method and support the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08945 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kernel Debiased Plug-in Estimation based on the Universal Least Favorable Submodel Chen, Haiyi Liu, Yang Malenica, Ivana Statistics Theory Machine Learning We propose ULFS-KDPE, a kernel debiased plug-in estimator based on the universal least favorable submodel, for estimating pathwise differentiable parameters in nonparametric models. The method constructs a data-adaptive debiasing flow in a reproducing kernel Hilbert space (RKHS), producing a plug-in estimator that achieves semiparametric efficiency without requiring explicit derivation or evaluation of efficient influence functions. We place ULFS-KDPE on a rigorous functional-analytic foundation by formulating the universal least favorable update as a nonlinear ordinary differential equation on probability densities. We establish existence, uniqueness, stability, and finite-time convergence of the empirical score along the induced flow. Under standard regularity conditions, the resulting estimator is regular, asymptotically linear, and attains the semiparametric efficiency bound simultaneously for a broad class of pathwise differentiable parameters. The method admits a computationally tractable implementation based on finite-dimensional kernel representations and principled stopping criteria. In finite samples, the combination of solving a rich collection of score equations with RKHS-based smoothing and avoidance of direct influence-function evaluation leads to improved numerical stability. Simulation studies illustrate the method and support the theoretical results. |
| title | Kernel Debiased Plug-in Estimation based on the Universal Least Favorable Submodel |
| topic | Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2603.08945 |