Abstract
In this article, we use the saddlepoint approximation method to compute the cumulative distribution function of non-central complex Wilks statistic. This approximation does not require conditions on the dimension, degrees of freedom, and non-centrality matrix. We also compare our results with known approximations to show the accuracy of our approximation. For applications, we compute the power functions of the Wilks statistic in the complex multivariate analysis of variance and the probability of detection of the Wilks detector in signal detection in noise model.
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