Appendix A kernel test for quasi independence

Appendix A: Preliminary results Appendix B: Proofs of sections 2 and 3 Appendix C: Proof of Theorem 4.1 (null distribution) Appendix D: Proof of Theorem 4.2 (consistency under alternatives) Appendix E: Efficient wild bootstrap implementation Appendix F: Review of related quasi-independence tests Appendix G: Additional experiments and discussion The following Proposition is an intermediate result, which is need to prove Lemmas C.3 and D.1. Let us consider the statement i). B.1 Proof of Proposition 2.1 Proof: From Equation (4), we have Ψ Before proving Theorem 4.1 we give some essential definitions which will be used by our proofs. Assume that K is bounded. The previous result, together with Lemma C.1, allow us to deduce Ψ C.2 Proof of Lemma C.1 In order to prove Lemma of C.1, we require some intermediate results.