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We show that the distribution of the scalar Schur complement in a noncentralWishart matrix is a mixture of central chi-square distributions with differentdegrees of freedom. For the case of a rank-1 noncentrality matrix, the weightsof the mixture representation arise from a noncentral beta mixture of Poissondistributions.

Chi-Square Mixture Representations for the Distribution of the Scalar Schur Complement in a Noncentral Wishart Matrix