A Novel Multivariate Goodness-of-Fit Test based on Mahalanobis Distance and Its Application in Denoising

Khuram Naveed, Naveed ur Rehman

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review


Existing multivariate goodness of fit (GoF) tests, to check for multivariate data normality, are cumbersome or intractable. Yet, they garner considerable interest in many practical applications. Mostly, the current multivariate GoF approaches are trivial extensions of their univariate counterparts thereby ignoring inter channel signal dependencies that are inherent in multivariate data sets. To address that, we develop a novel multivariate goodness of fit (GoF) test that uses Mahalanobis distance (MD) as a transformation to map multivariate data into a univariate time series. This way, a novel multivariate GoF test is defined based on the premise that EDF of MD computed for multichannel data are distinct. To test for normality, CDF of quadratic transformation of multivariate normal random variables is used as the reference model within the Anderson Darling (AD) statistic. Finally, this test is used on multiple scales to reject multivariate coefficients fitting the normal distribution leading to a novel multivariate signal denoising method.

Original languageUndefined/Unknown
Title of host publication29th European Signal Processing Conference, EUSIPCO 2021 - Proceedings
Number of pages5
Publication date1 Aug 2021
ISBN (Electronic)9789082797060
Publication statusPublished - 1 Aug 2021


  • Denoising
  • Goodness-of-fit test
  • Mahalanobis distance
  • Multivariate signals

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