Year: 2026
Type: article
Abstract: ABSTRACT Matrix‐valued data, where each observation is represented as a matrix, frequently arises in various scientific disciplines. Modelling such data often relies on matrix‐variate normal distributions, making matrix‐variate normality testing crucial for valid statistical inference. Recently, the Distance‐Distance (DD) plot has been introduced as a graphical tool for visually assessing matrix‐variate normality. However, the Mahalanobis‐squared distances (MSD) used in the DD plot require vectorizing matrix observations, restricting its applicability to cases where the dimension of the vectorized data does not exceed the sample size. To address this limitation, we propose a novel graphical method called the Matrix Healy (MatHealy) plot, an extension of the Healy plot for vector‐valued data. This new plot is based on matrix‐based MSD that leverages the inherent structure of matrix data. Consequently, it offers a more reliable visual assessment. Importantly, the MatHealy plot eliminates the sample size restriction of the DD plot and hence more applicable to matrix‐valued data. Empirical results demonstrate its effectiveness and practicality compared to the DD plot across various scenarios, particularly in cases where the DD plot is not available due to limited sample sizes.
DOI: 10.1111/anzs.70068
Authors: Fen Jiang, Jianhua Zhao, Changchun Shang, Xuan Ma, Yue Wang, Ye Tao
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,970
OpenAlex ID: W6891868573
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