Normality Testing of High-Dimensional Data Based on Principle Component and Jarque–Bera Statistics
| Autor: | Ya-nan Song, Xuejing Zhao |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Clustering high-dimensional data
Computer science principal component media_common.quotation_subject 05 social sciences empirical power Multivariate normal distribution Sample (statistics) simulation 01 natural sciences Jarque–Bera statistic 010104 statistics & probability Normality test 0502 economics and business Jarque–Bera test Statistics Principal component analysis 050207 economics 0101 mathematics lcsh:Statistics lcsh:HA1-4737 Independence (probability theory) Normality normality testing media_common |
| Zdroj: | Stats, Vol 4, Iss 16, Pp 216-227 (2021) Stats Volume 4 Issue 1 Pages 16-227 |
| ISSN: | 2571-905X |
| DOI: | 10.3390/stats4010016 |
| Popis: | The testing of high-dimensional normality is an important issue and has been intensively studied in the literature, it depends on the variance–covariance matrix of the sample and numerous methods have been proposed to reduce its complexity. Principle component analysis (PCA) has been widely used in high dimensions, since it can project high-dimensional data into a lower-dimensional orthogonal space. The normality of the reduced data can then be evaluated by Jarque–Bera (JB) statistics in each principle direction. We propose a combined test statistic—the summation of one-way JB statistics upon the independence of the principle directions—to test the multivariate normality of data in high dimensions. The performance of the proposed method is illustrated by the empirical power of the simulated normal and non-normal data. Two real data examples show the validity of our proposed method. |
| Databáze: | OpenAIRE |
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