Asymptotic distributions of the sphericity test in a complex multivariate normal distribution |
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Authors: | C Fang PR Krishnaiah BN Nagarsenker |
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Institution: | 1. University of Pittsburgh , Pittsburgh, Pennsylvania;2. Air Force Institute of Technology , Wright-Patterson Air Force Base, Ohio |
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Abstract: | In this paper, asymptotic expansions of the null and non-null distributions of the sphericity test criterion in the case of a complex multivariate normal distribution are obtained for the first time in terms of beta distributions. In the null case, it is found that the accuracy of the approximation by taking the first term alone in the asymptotic series is sufficient for practical purposes. In fact for p - 2. the asymptotic expansion reduces to the first term which is also the exact distribution in this case. Applications of the results to the area of inferences on multivariate time series are also given. |
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Keywords: | likelihood ratio criterion asymptotic expansion null distribution non-null distribution beta distribution |
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