TY - JOUR
T1 - Empirical likelihood method for complete independence test on high-dimensional data
AU - Qi, Yongcheng
AU - Zhou, Yingchao
N1 - Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2022
Y1 - 2022
N2 - Given a random sample of size n from a p dimensional random vector, we are interested in testing whether the p components of the random vector are mutually independent. This is the so-called complete independence test. In the multivariate normal case, it is equivalent to testing whether the correlation matrix is an identity matrix. In this paper, we propose a one-sided empirical likelihood method for the complete independence test based on squared sample correlation coefficients. The limiting distribution for our one-sided empirical likelihood test statistic is proved to be (Formula presented.) when both n and p tend to infinity, where Z is a standard normal random variable. In order to improve the power of the empirical likelihood test statistic, we also introduce a rescaled empirical likelihood test statistic. We carry out an extensive simulation study to compare the performance of the rescaled empirical likelihood method and two other statistics.
AB - Given a random sample of size n from a p dimensional random vector, we are interested in testing whether the p components of the random vector are mutually independent. This is the so-called complete independence test. In the multivariate normal case, it is equivalent to testing whether the correlation matrix is an identity matrix. In this paper, we propose a one-sided empirical likelihood method for the complete independence test based on squared sample correlation coefficients. The limiting distribution for our one-sided empirical likelihood test statistic is proved to be (Formula presented.) when both n and p tend to infinity, where Z is a standard normal random variable. In order to improve the power of the empirical likelihood test statistic, we also introduce a rescaled empirical likelihood test statistic. We carry out an extensive simulation study to compare the performance of the rescaled empirical likelihood method and two other statistics.
KW - complete independence test
KW - Empirical likelihood
KW - high-dimension
KW - multivariate normal distribution
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U2 - 10.1080/00949655.2022.2029860
DO - 10.1080/00949655.2022.2029860
M3 - Article
AN - SCOPUS:85124133356
JO - Journal of Statistical Computation and Simulation
JF - Journal of Statistical Computation and Simulation
SN - 0094-9655
ER -