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A practice-oriented guide to statistical inference in linear modeling for non-normal or heteroskedastic error

Hanna Rajh-Weber1, Stefan Ernest Huber2, Martin Arendasy2

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Summary

Applied researchers face challenges when classical statistical methods fail. This study compares standard hypothesis tests with alternatives like HC3, HC4, and bootstrap methods for ordinary least squares regression under assumption violations.

Keywords:
BootstrapLinear regressionRobust inferenceSimulationViolated assumptions

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Area of Science:

  • Statistics
  • Econometrics
  • Data Science

Background:

  • Applied researchers often encounter violations of classical statistical assumptions like normality and homoskedasticity.
  • Selecting appropriate statistical methods under these conditions is a significant challenge.

Purpose of the Study:

  • To compare the performance of classical hypothesis tests with alternative inference methods for ordinary least squares (OLS) regression.
  • To provide guidelines for selecting statistical methods when distributional assumptions are violated.

Main Methods:

  • Comparison of classical hypothesis tests with HC3, HC4, and six bootstrap methods.
  • Assessment across four regression models with varying non-normality and heteroskedasticity.
  • Evaluation using five sample sizes (25 to 500) and 10,000 generated samples per scenario.

Main Results:

  • No single method performed optimally across all tested scenarios.
  • HC3/HC4 standard errors and wild bootstrap with percentile confidence intervals showed reliability in many situations.
  • Performance varied significantly based on the degree of assumption violation and sample size.

Conclusions:

  • Researchers should consider alternative methods like HC3, HC4, or bootstrap when OLS assumptions are violated.
  • Method selection should be guided by the specific data situation and the performance tables provided.
  • No universal best method exists; context-specific choices are crucial for reliable statistical inference.