Kernel Debiased Plug-in Estimation based on the Universal Least Favorable Submodel

• URL: http://arxiv.org/abs/2603.08945v1
• Date: Mon, 09 Mar 2026 21:27:26 GMT
• Title: Kernel Debiased Plug-in Estimation based on the Universal Least Favorable Submodel
• Abstract summary: We present a kernel debiased plug-in estimator for estimating pathwise differentiable parameters in nonparametric models.<n>The method achieves semiparametric efficiency without requiring explicit derivation or evaluation of efficient influence functions.
• Score: 4.609717518771183
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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