Application of integral operator for regularized least-square regression

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Control functionals for Monte Carlo integration (2014, methodology): “T(f 1 f^ 1) + ^c: This completes the proof. Proof of Theorem 4. Unbiasedness follows from (A1,3) by applying the conclusions of Theorem 1 and Lemma 1. For the variance we appeal to the main result of Sun and Wu (2009), who considered convergence in the general setting where Xis not assumed to be com”
Approximation of eigenfunctions in kernel-based spaces (2014, unknown): “The following theorem (see e.g. [20, Ch. 5]) applies to our situation, and provides a way to represent the kernel as an expansion (or Hilbert - Schmidt or Mercer ) kernel (see e.g. [23, 22]).”