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Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine
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Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine

Published on: January 5, 2024

One-Step Estimation of Differentiable Hilbert-Valued Parameters.

Alex Luedtke1, Incheoul Chung1

  • 1Department of Statistics, University of Washington.

Annals of Statistics
|June 29, 2026
PubMed
Summary
This summary is machine-generated.

We developed new statistical estimators for smooth Hilbert-valued parameters, offering efficient estimation and confidence sets even with machine learning nuisance estimators. These methods apply to reproducing kernel Hilbert spaces and beyond, addressing challenges in causal inference.

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Last Updated: Jun 30, 2026

Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine
08:27

Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine

Published on: January 5, 2024

Area of Science:

  • Statistics
  • Machine Learning
  • Causal Inference

Background:

  • Statistical estimation of smooth Hilbert-valued parameters is crucial in various fields.
  • Pathwise differentiability is a key condition for developing robust estimators.
  • Existing methods may struggle with nuisance parameters or spaces lacking reproducing kernels.

Purpose of the Study:

  • To develop efficient, root-n rate estimators and confidence sets for smooth Hilbert-valued parameters.
  • To provide theoretical guarantees for these estimators, even when using machine learning techniques for nuisance functions.
  • To extend estimation methods to Hilbert spaces without reproducing kernels and address parameters lacking efficient influence functions.

Main Methods:

  • Utilizing pathwise differentiability to characterize parameter smoothness.
  • Generalizing cross-fitted one-step estimators based on Hilbert-valued efficient influence functions.
  • Proposing a regularized one-step estimator for cases without efficient influence functions.

Main Results:

  • Achieved efficient, root-n rate estimators and confidence sets in reproducing kernel Hilbert spaces.
  • Demonstrated theoretical guarantees for estimators using arbitrary nuisance function estimators, including machine learning methods.
  • Extended results to Hilbert spaces lacking reproducing kernels and introduced a novel regularized estimator for challenging cases.
  • Confirmed pathwise differentiability for several parameters relevant to causal inference.

Conclusions:

  • The proposed estimators offer efficient statistical inference for smooth Hilbert-valued parameters.
  • The methods are robust to the use of machine learning for nuisance functions.
  • New tools are provided for causal inference, including estimators for counterfactual density and dose-response functions.