Appendix B : Proof of Theorem 2
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چکیده
منابع مشابه
Functional wavelet regression for linear function-on-function models
1 Appendix B: Additional proofs of theorems . . . . . . . . . . . . . . . 2 1.1 Proof of Theorem 4.2 . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Proof of Theorem 4.3 . . . . . . . . . . . . . . . . . . . . . . . . . 17 2 Appendix D: Proofs of technical lemmas . . . . . . . . . . . . . . . . . 21 3 Appendix C: Additional simulation . . . . . . . . . . . . . . . . . . . . 44 4 Appendi...
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In this appendix, we prove Theorem 4 and Lemmas 7 – 12 in order. A.1. Proof of Theorem 4. We first need a lemma for perturbation bound of square root matrices. Lemma 16. Let A, B be positive semi-definite matrices, and then for any unitarily invariant norm ï¿¿·ï¿¿, ï¿¿A 1/2 − B 1/2 ï¿¿ ≤ 1 σ min (A 1/2) + σ min (B 1/2) ï¿¿A − Bï¿¿. Proof. The proof essentially follows the idea of [27]. Let D = ...
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تاریخ انتشار 2016