Inequalities for spreads of matrix sums and products.

By J. Merikoski, Ravinder Kumar. 2004

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Identifying Cointegration by Eigenanalysis (2015, unknown): “Π−d n ) EnE ′ nΠ −d n V j. Let δ 1 ≤ ··· ≤ δn and γ 1 ≥ ··· ≥ γn be the eigenvalues of ΠnΠ ′ n and (Π −d n ) ′E nE ′ nΠ −d n respectively. Since λ 1(EnE′ n) = ··· = λn−1(EnE ′ n) = 1, by Theorem 9 of Merikoski and Kumar (2004), it follows that δ−d i+1 = λi+1((Π −d n ) ′Π−d n )λn−1(EnE ′ n) ≤ γi ≤ λi”
On rates of convergence in functional linear regression (2007, background): “It follows from Theorem 7 of Merikoski and Kumar [13] that (2K+1)−i+1 −1i for all i.”