A Goodness-of-Fit Test for Independent Component Models in High Dimensions

2026-05-19

AI Summary

This study addresses the lack of theoretically grounded goodness-of-fit tests for high-dimensional independent component analysis, particularly when the data dimension grows proportionally with the sample size. The authors propose a novel goodness-of-fit test that eliminates the need for pre-whitening—a longstanding requirement in conventional approaches—and establish, for the first time, a theoretically valid testing procedure within a high-dimensional asymptotic framework. The test statistic is constructed based on high-dimensional asymptotic theory, and extensive numerical simulations demonstrate its reliable size control and strong power across various settings. Empirical analysis further highlights the method’s practical diagnostic potential in real-world applications, such as gene expression data analysis.

Abstract

Independent component (IC) models are a standard tool for representing multivariate data in statistics, signal processing, and machine learning. Despite the extensive use of IC models, much less attention has been given to goodness-of-fit tests for assessing their compatibility with data. We develop the first goodness-of-fit test for IC models that is supported by a theoretical validity guarantee when the data dimension and sample size diverge proportionally. This is made possible by the fact that the test does not rely on a pre-whitening step, which often limits the applicability of other goodness-of-fit tests in high dimensions. Our theoretical analysis is complemented with numerical experiments that demonstrate the test's size control and power under a range of conditions. In addition, we provide examples involving gene-expression data to illustrate that the test has potential for effective diagnostic use in practice.

Problem

• goodness-of-fit test
• independent component models
• high dimensions
• model compatibility
• statistical validation

Innovation

• goodness-of-fit test
• independent component analysis
• high-dimensional statistics
• pre-whitening-free
• theoretical validity