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

TY - GEN

T1 - A Novel Multivariate Goodness-of-Fit Test based on Mahalanobis Distance and Its Application in Denoising

AU - Naveed, Khuram

AU - Rehman, Naveed ur

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Multivariate signals

KW - Denoising

KW - Mahalanobis distance

KW - Goodness-of-fit test

M3 - Conference article

SN - 2076-1465

SP - 2050

EP - 2054

JO - European Signal Processing Conference

JF - European Signal Processing Conference

T2 - 29th European Signal Processing Conference (EUSIPCO)

Y2 - 23 August 2021 through 27 August 2021

ER -