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

TL;DR

This paper introduces ULFS-KDPE, a kernel-based debiased estimator for nonparametric models that achieves semiparametric efficiency without explicit influence function derivation, supported by theoretical guarantees and simulations.

Contribution

It develops a novel data-adaptive debiasing flow in RKHS using a nonlinear ODE framework, enabling efficient estimation of pathwise differentiable parameters.

Findings

Achieves semiparametric efficiency bounds.

Provides a stable, finite-sample implementation.

Demonstrates improved numerical stability in simulations.

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.