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Significance Tests for Boosted Location and Scale Models with Linear Base-Learners.

Tobias Hepp1,2, Matthias Schmid1, Andreas Mayr1

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The International Journal of Biostatistics
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Summary

This study introduces novel permutation tests and bootstrap methods to generate p-values for gradient boosting in distributional regression. These techniques enable reliable statistical inference for generalized additive models for location, scale, and shape (GAMLSS) in biostatistical analyses.

Keywords:
GAMLSSboostingparametric bootstrappermutation testregularized regression

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Area of Science:

  • Statistical modeling
  • Biostatistics
  • Machine learning

Background:

  • Generalized additive models for location, scale, and shape (GAMLSS) provide flexible statistical analysis but face challenges in model specification.
  • Gradient boosting algorithms simplify GAMLSS specification but yield shrunken estimates, complicating confidence intervals and test statistics.

Purpose of the Study:

  • To propose and evaluate methods for obtaining p-values for linear effect estimates in Gaussian GAMLSS using gradient boosting.
  • To address the challenge of statistical inference in distributional regression models applied to biostatistical data.

Main Methods:

  • Development of two strategies: permutation tests and a parametric bootstrap approach.
  • Application to Gaussian location and scale models within the GAMLSS framework.
  • Simulation studies for low- and high-dimensional data, and an epidemiological study.

Main Results:

  • Both permutation tests and bootstrap methods successfully controlled the type-I error rate in simulations.
  • Reasonable test power was achieved in low-dimensional data, comparable to maximum likelihood inference.
  • In high-dimensional settings, power decreased but type-I error remained controlled, offering a feasible inference method.

Conclusions:

  • The proposed permutation and bootstrap tests offer viable solutions for calculating p-values in gradient boosting for GAMLSS.
  • These methods facilitate robust statistical inference in distributional regression, particularly in biostatistical applications.
  • The study demonstrates practical application in analyzing lung function in an elderly German cohort.