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Supplemental Material for Inference Based on Conditional Moment Inequalities



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Supplement to INFERENCE BASED ON CONDITIONAL MOMENT INEQUALITIES By Donald W K Andrews and Xiaoxia Shi June 2010 COWLES FOUNDATION DISCUSSION PAPER NO 1761S COWLES FOUNDATION FOR RESEARCH IN ECONOMICS YALE UNIVERSITY Box 208281 New Haven Connecticut 06520 8281 http cowles econ yale edu Supplemental Material for Inference Based on Conditional Moment Inequalities Donald W K Andrews Cowles Foundation for Research in Economics Yale University Xiaoxia Shi Department of Economics Yale University November 2007 Revised June 2010 11 Outline This Supplement includes ve appendices The rst appendix Appendix B provides a number of supplemental results to the main paper These include i results for Kolmogorov Smirnov KS and approximate Cram r von Mises ACvM tests and CS s in Section 12 1 ii three additional examples of collections G and probability measures Q that satisfy Assumptions CI M FA e and Q in Section 12 2 iii an illustration of the veri cation of Assumptions LA1 LA3 in Section 12 3 iv an illustration of some uniformity issues that arise with in nite dimensional nuisance parameters in Section 12 4 v an illustration of problems with pointwise asymptotics in Section 12 5 and vi coverage probability results for subsampling tests and CS s under drifting sequences of distributions in Section 12 6 Appendix C provides proofs of the results that are stated in the main paper but are not proved in Appendix A These include i the proofs of Lemmas 2 and 3 and Theorem 2 b in Section 13 1 ii the proofs of Lemma 4 and Theorem 3 concerning xed alternatives in Section 13 2 iii the proof of Theorem 4 concerning local power in Section 13 3 and iv the proof of Lemma 1 concerning the veri cation of Assumptions S1 S4 in Section 13 4 Appendix D provides proofs of the results stated in Appendix B These include i the proofs of Kolmogorov Smirnov and approximate Cram r von Mises results in Section 14 1 ii the proof of Lemma B2 in Section 14 2 iii the proofs of Theorems B4 and B5 regarding



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