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Testing multivariate normality using angular skewness and kurtosis processes

Abstract Number:

1785 

Submission Type:

Contributed Abstract 

Contributed Abstract Type:

Paper 

Participants:

Jisu Oh (1), Subhashis Ghoshal (1)

Institutions:

(1) North Carolina State University, N/A

Co-Author:

Subhashis Ghoshal  
North Carolina State University

First Author:

Jisu Oh  
North Carolina State University

Presenting Author:

Jisu Oh  
North Carolina State University

Abstract Text:

Given a sample X_1, ... , X_n from a common distribution P in R^d, d ≥ 2, we develop a method to test multivariate normality based on two random processes S_n and K_n indexed by the unit sphere S^{d-1}, which stand respectively for the skewness and kurtosis of linear combinations. We show that the limit processes are Gaussian and can be represented as random finite linear combinations of the spherical harmonics. We consider test statistics based on the supremums of these processes and numerically obtain their limit distributions. We also show that the Bayesian bootstrap can consistently estimate the cutoffs. We obtain the limiting power of the test under contiguous alternative hypotheses. Through an extensive simulation study, we show that our proposed method performs well for moderate and large sample sizes.

Keywords:

multivariate normality test|skewness and kurtosis|stochastic processes|spherical harmonics| emprical processes| Bayesian bootstrap

Sponsors:

IMS

Tracks:

Statistical Theory

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