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Updated: Jan 26, 2026

Author Spotlight: Functionalizing Metal-Organic Frameworks: Advancements, Challenges, and the Power of Post-Synthetic Ligand Exchange
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UNIFORMLY VALID POST-REGULARIZATION CONFIDENCE REGIONS FOR MANY FUNCTIONAL PARAMETERS IN Z-ESTIMATION FRAMEWORK.

Alexandre Belloni1, Victor Chernozhukov2, Denis Chetverikov3

  • 1Fuqua School of Business, Duke University, 100 Fuqua Drive, Durham, North Carolina 27708, USA, abn5@duke.edu.

Annals of Statistics
|April 9, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces novel procedures for constructing simultaneous confidence bands for high-dimensional parameters in moment condition models. The method uses Neyman orthogonality and multiplier bootstrap for efficient inference, especially with functional data.

Keywords:
Inference after model selectionLasso and Post-Lasso with functional response datamoment condition models with a continuum of target parameters

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Area of Science:

  • Econometrics
  • Statistics
  • Machine Learning

Background:

  • Inference for high-dimensional parameters (where the number of parameters, p, is much larger than the sample size, n) is challenging, especially in moment condition models.
  • Existing methods often struggle with functional response data and large-scale parameter spaces, limiting their applicability.
  • Model selection further complicates inference, requiring robust procedures that account for potential parameter uncertainty.

Purpose of the Study:

  • To develop statistically sound and computationally efficient procedures for constructing simultaneous confidence bands for potentially infinite-dimensional parameters in general moment condition models.
  • To extend these procedures to settings with functional response data and high-dimensional parameters (p >> n).
  • To provide a general framework applicable to complex models, such as distribution regression.

Main Methods:

  • Construction of score functions that approximately satisfy the Neyman orthogonality condition.
  • Utilization of uniform central limit theorems for high-dimensional vectors to establish the validity of the confidence bands.
  • Implementation of a computationally efficient multiplier bootstrap procedure for constructing the bands, avoiding repeated high-dimensional optimization.

Main Results:

  • The proposed procedures yield valid simultaneous confidence bands even when the number of parameters is potentially infinite or much larger than the sample size.
  • The multiplier bootstrap method is shown to be computationally efficient, relying only on resampling estimated score functions.
  • The general theory is successfully applied to the distribution regression model with a logistic link, demonstrating practical applicability.

Conclusions:

  • The developed methodology provides a robust framework for simultaneous inference in high-dimensional moment condition models, including those with functional data.
  • The multiplier bootstrap offers a computationally feasible approach for constructing confidence bands in these complex settings.
  • The findings are illustrated through simulations and a real-world data application, confirming the practical utility of the proposed methods.