Kronecker delta method for testing independence between two vectors in high-dimension

Ivair R. Silva (), Yan Zhuang and Julio C. A. da Silva Junior
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Ivair R. Silva: Federal University of Ouro Preto
Yan Zhuang: Connecticut College
Julio C. A. da Silva Junior: Federal University of Vicosa

Statistical Papers, 2022, vol. 63, issue 2, No 1, 343-365

Abstract: Abstract Conventional methods for testing independence between two Gaussian vectors require sample sizes greater than the number of variables in each vector. Therefore, adjustments are needed for the high-dimensional situation, where the sample size is smaller than the number of variables in at least one of the compared vectors. It is critical to emphasize that the methods available in the literature are unable to control the Type I error probability under the nominal level. This fact is evidenced through an intensive simulation study presented in this paper. To cover this lack, we introduce a valid randomized test based on the Kronecker delta covariance matrices estimator. As an empirical application, based on a sample of companies listed on the stock exchange of Brazil, we test the independence between returns of stocks of different sectors in the COVID-19 pandemic context.

Keywords: Kronecker delta covariance structure; Randomized testing; High-dimensional Data; Multivariate Gaussian Vectors (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00362-021-01238-z

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