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A Test to Determine the Multivariate Normality of a Data Set
September 1988 (vol. 10 no. 5)
pp. 757-761
ASCII Text
x 
 
S.P. Smith, A.K. Jain, "A Test to Determine the Multivariate Normality of a Data Set," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 5, pp. 757-761, September, 1988.
 
 
BibTex
x
 
@article{ 10.1109/34.6789,
author = {S.P. Smith and A.K. Jain},
title = {A Test to Determine the Multivariate Normality of a Data Set},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {10},
number = {5},
issn = {0162-8828},
year = {1988},
pages = {757-761},
doi = {http://doi.ieeecomputersociety.org/10.1109/34.6789},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - A Test to Determine the Multivariate Normality of a Data Set
IS - 5
SN - 0162-8828
SP757
EP761
EPD - 757-761
A1 - S.P. Smith,
A1 - A.K. Jain,
PY - 1988
KW - Monte Carlo method; multivariate normality; data set; pattern recognition; Wald-Wolfowitz; spanning tree; interpopulation; test statistic; interpolation; Monte Carlo methods; pattern recognition; trees (mathematics)
VL - 10
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 

A test is described for multivariate normality that is useful in pattern recognition. The test is based on the Friedman-Rafsky (1979) multivariate extension of the Wald-Wolfowitz runs test. The test data are combined with a multivariate swarm of points following the normal distribution generated with mean vector and covariance matrix estimated from the test data. The minimal spanning tree of this resultant ensemble of points is computed and the count of the interpopulation edges in the minimal spanning tree is used as a test statistic. The simulation studied both the null case of the test and one simple deviation from normality. Two conclusions are made from this study. First, the test can be conservatively applied by using the asymptotic normality of the test statistic, even for small sample sizes. Second, the power of the test appears reasonable, especially in high dimensions. Monte Carlo experiments were performed to determine if the test is reliable in high dimensions with moderate sample size. The method is compared to other such tests available in the literature.

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Index Terms:
Monte Carlo method; multivariate normality; data set; pattern recognition; Wald-Wolfowitz; spanning tree; interpopulation; test statistic; interpolation; Monte Carlo methods; pattern recognition; trees (mathematics)
Citation:
S.P. Smith, A.K. Jain, "A Test to Determine the Multivariate Normality of a Data Set," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 5, pp. 757-761, Sept. 1988, doi:10.1109/34.6789
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