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(iii) Clarification: the result of Theorem 3.1 holds along sequences θ(τ) = τh, τ → 0, along which the directional derivatives of the eigenvalues in direction h ∈ R >0 do not vanish; that is, d/dτ|τ=0λj(τh) ̸ = 0, j = 2, . . . , n. The vector 1 := (1, . . . , 1) serves here and in the following as a place holder butmaywithout loss of generality be replaced throughout by any other fixed direction h ∈ R >0 with the above property. This comment applies to all the following results in the paper accordingly. In general, the eigenvalue decomposition is guaranteed to be differentiable only for correlation models that are real analytic in θ(τ); see [1, Sections 7.2 and 7.7]. The method of Van Der Aa et al., referenced as [22] in the original paper, works to compute eigenvector derivatives formultiple eigenvalues, provided that, for some order k ∈ N, the kth-order derivatives of the eigenvalues are mutually distinct.

Erratum to “Asymptotic Behavior of the Likelihood Function of Covariance Matrices of Spatial Gaussian Processes”