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A simultaneous confidence-bounded true discovery proportion perspective on localizing differences in smooth terms in

David Swanson1

  • 1University of Texas MD Anderson Cancer Center, Houston, TX, USA.

Computational Statistics & Data Analysis
|June 20, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method for identifying differences between two smooths using true discovery proportion (TDP) estimation. The approach provides confidence-bounded statements on the proportion of true differences in specific regions, enhancing statistical rigor.

Keywords:
closed-testingmultiple testingsimultaneous confidencesmoothingsplines

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Area of Science:

  • Statistical modeling
  • Nonparametric regression analysis
  • Data interpretation

Background:

  • Accurate localization of differences between smooth functions is crucial in statistical analysis.
  • Existing methods often rely on ad hoc approaches, such as data subsetting and hypothesis testing, which can lack rigor.
  • There is a need for statistically sound methods to quantify regions of divergence between smooth terms.

Purpose of the Study:

  • To develop and demonstrate a method for localizing differences between two spline terms (smooths).
  • To provide confidence-bounded statements on the proportion of true differences within specific regions.
  • To offer a statistically rigorous alternative to ad hoc methods for comparing smooths.

Main Methods:

  • Utilizes a true discovery proportion (TDP)-based interpretation for localization.
  • Employs a closed-testing procedure based on the Simes local test.
  • Relies on multivariate chi-squared test statistics of generalized Wishart type, assuming positive regression dependence on subsets (PRDS).

Main Results:

  • The method yields statements on the proportion of regions where true differences exist between smooths.
  • TDP estimates are simultaneously confidence-bounded (1-α), providing lower bounds on true discoveries with high confidence.
  • Demonstrates consistency for generalized additive models with tuning parameters selected by REML or GCV.

Conclusions:

  • The proposed method offers a statistically robust approach for identifying and quantifying differences between smooths.
  • The confidence-bounded TDP provides reliable estimates of true discoveries, irrespective of the number of comparisons made.
  • The methodology is validated through simulation studies and applied to analyze walking gait data.