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To prove the lemma, it suffices to show that the Hessian ∇ $^{2}$G is positive semidefinite. We need to show that all the principal minors of ∇ $^{2}$G in (76) are nonnegative. 

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However, because we already know that all the principal minors of the matrix in (75) are nonnega- tive, it only remains to show that ∂ $^{2}$G ∂µ 2 ≥ 0 and det ∇ $^{2}$G ≥ 0 . 

First, we show that ∂ $^{2}$G ∂µ 2 ≥ 0 Find the first derivative of G. 

Find the second derivative of G . 

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The denominator of (79) is positive. Hence, it only remains to show that the numerator is nonneg- 

