The Morgan-Pitman Test of Equality of Variances and its Application to Machine Learning Model Evaluation and Selection

• URL: http://arxiv.org/abs/2509.12185v1
• Date: Mon, 15 Sep 2025 17:47:38 GMT
• Title: The Morgan-Pitman Test of Equality of Variances and its Application to Machine Learning Model Evaluation and Selection
• Authors: Argimiro Arratia, Alejandra Cabaña, Ernesto Mordecki, Gerard Rovira-Parra,
• Abstract summary: We propose the use of a statistical test to assess the equality of variances in forecasting errors.<n>The test builds upon the classic Morgan-Pitman approach, incorporating enhancements to ensure robustness against data with heavy-tailed distributions or outliers.
• Score: 39.146761527401424
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Model selection in non-linear models often prioritizes performance metrics over statistical tests, limiting the ability to account for sampling variability. We propose the use of a statistical test to assess the equality of variances in forecasting errors. The test builds upon the classic Morgan-Pitman approach, incorporating enhancements to ensure robustness against data with heavy-tailed distributions or outliers with high variance, plus a strategy to make residuals from machine learning models statistically independent. Through a series of simulations and real-world data applications, we demonstrate the test's effectiveness and practical utility, offering a reliable tool for model evaluation and selection in diverse contexts.

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