A test for multivariate normality based on sample entropy and projection pursuit

Li-Xing Zhu; Hoi Lam Wong; Kai-Tai Fang

doi:10.1016/0378-3758(94)00058-4

A test for multivariate normality based on sample entropy and projection pursuit

Li-Xing Zhu, Hoi Lam Wong, Kai-Tai Fang^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

31 Citations (Scopus)

Abstract

Testing normality and multinormality has long been an interesting issue in statistical inferences. Many tests have been proposed. In particular, Vasicek (J. Roy. Statist. Soc. A 139 (1976), 54-59) suggested a test based on sample entropy. A similar idea was extended to the multivariate case with projection pursuit for searching for departure from the multivariate normal distribution. We, in this paper, suggest a new test for multinormality based on density estimation, a number-theoretic method, projection pursuit technique and sample entropy. Our results show that the new test may be recommended for practice.

Original language	English
Pages (from-to)	373-385
Number of pages	13
Journal	Journal of Statistical Planning and Inference
Volume	45
Issue number	3
DOIs	https://doi.org/10.1016/0378-3758(94)00058-4
Publication status	Published - Jun 1995

Scopus Subject Areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

User-Defined Keywords

62G10
62H40
65C05
Density estimation
Entropy
Kurtosis
Multivariate normality
Number-theoretic method
Projection pursuit
Skewness

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10.1016/0378-3758(94)00058-4

Cite this

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title = "A test for multivariate normality based on sample entropy and projection pursuit",

abstract = "Testing normality and multinormality has long been an interesting issue in statistical inferences. Many tests have been proposed. In particular, Vasicek (J. Roy. Statist. Soc. A 139 (1976), 54-59) suggested a test based on sample entropy. A similar idea was extended to the multivariate case with projection pursuit for searching for departure from the multivariate normal distribution. We, in this paper, suggest a new test for multinormality based on density estimation, a number-theoretic method, projection pursuit technique and sample entropy. Our results show that the new test may be recommended for practice.",

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author = "Li-Xing Zhu and Wong, {Hoi Lam} and Kai-Tai Fang",

note = "Funding Information: This work was supported by the Hong Kong UPGC grant, the Croucher Foundation of Hong Kong and the NSF of China. * Corresponding author.",

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AU - Zhu, Li-Xing

AU - Wong, Hoi Lam

AU - Fang, Kai-Tai

N1 - Funding Information: This work was supported by the Hong Kong UPGC grant, the Croucher Foundation of Hong Kong and the NSF of China. * Corresponding author.

PY - 1995/6

Y1 - 1995/6

N2 - Testing normality and multinormality has long been an interesting issue in statistical inferences. Many tests have been proposed. In particular, Vasicek (J. Roy. Statist. Soc. A 139 (1976), 54-59) suggested a test based on sample entropy. A similar idea was extended to the multivariate case with projection pursuit for searching for departure from the multivariate normal distribution. We, in this paper, suggest a new test for multinormality based on density estimation, a number-theoretic method, projection pursuit technique and sample entropy. Our results show that the new test may be recommended for practice.

AB - Testing normality and multinormality has long been an interesting issue in statistical inferences. Many tests have been proposed. In particular, Vasicek (J. Roy. Statist. Soc. A 139 (1976), 54-59) suggested a test based on sample entropy. A similar idea was extended to the multivariate case with projection pursuit for searching for departure from the multivariate normal distribution. We, in this paper, suggest a new test for multinormality based on density estimation, a number-theoretic method, projection pursuit technique and sample entropy. Our results show that the new test may be recommended for practice.

KW - 62G10

KW - 62H40

KW - 65C05

KW - Density estimation

KW - Entropy

KW - Kurtosis

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KW - Number-theoretic method

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KW - Skewness

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DO - 10.1016/0378-3758(94)00058-4

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JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

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A test for multivariate normality based on sample entropy and projection pursuit

Abstract

Scopus Subject Areas

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