Abstract
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.
Original language | English (US) |
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Pages (from-to) | 2386-2402 |
Number of pages | 17 |
Journal | Journal of Statistical Computation and Simulation |
Volume | 92 |
Issue number | 11 |
DOIs | |
State | Published - 2022 |
Bibliographical note
Publisher Copyright:© 2022 Informa UK Limited, trading as Taylor & Francis Group.
Keywords
- Empirical likelihood
- complete independence test
- high-dimension
- multivariate normal distribution