\relax 
\citation{GMZ}
\citation{LSW}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{\large Online Appendices to ``Testing for a General Class of Functional Inequalities''}}{A-1}}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{A}{Proofs of Theorems \ref {Thm1}-\ref {Thm5}}}{A-1}}
\newlabel{appendix-proof-A}{{A}{A-1}}
\newlabel{s and s_star}{{A.1}{A-2}}
\newlabel{v}{{A.2}{A-3}}
\newlabel{eq35}{{A.3}{A-3}}
\newlabel{inet}{{A.4}{A-4}}
\newlabel{dec45}{{A.5}{A-4}}
\newlabel{ineq54}{{A.6}{A-4}}
\newlabel{ineqs2}{{A.7}{A-5}}
\newlabel{decomp2}{{A.8}{A-5}}
\citation{Massart:07}
\citation{Chen/Linton/VanKeilegom:03}
\citation{Massart:07}
\newlabel{bd5}{{A.10}{A-7}}
\citation{Gine/Zinn:90}
\citation{Gine:97}
\newlabel{lambe}{{A.11}{A-9}}
\newlabel{atilde}{{A.12}{A-9}}
\newlabel{sigmae}{{A.13}{A-9}}
\newlabel{theta_hate}{{A.14}{A-9}}
\newlabel{theta*e}{{A.15}{A-10}}
\newlabel{dec56}{{A.16}{A-11}}
\newlabel{conv}{{A.17}{A-11}}
\citation{Linton/Song/Whang:10}
\newlabel{c_tildee*}{{A.18}{A-12}}
\newlabel{ineq42b}{{A.19}{A-14}}
\newlabel{comp}{{A.20}{A-14}}
\newlabel{comp2}{{A.21}{A-14}}
\newlabel{limit}{{A.22}{A-14}}
\newlabel{control}{{A.23}{A-14}}
\newlabel{probs}{{A.24}{A-15}}
\newlabel{cv33}{{A.25}{A-17}}
\newlabel{cv22}{{A.26}{A-17}}
\newlabel{a}{{A.27}{A-18}}
\newlabel{cv7}{{A.28}{A-18}}
\newlabel{c_ehta}{{A.29}{A-18}}
\newlabel{min}{{A.30}{A-19}}
\newlabel{v_sigh_0}{{A.31}{A-20}}
\newlabel{vrate}{{A.32}{A-20}}
\newlabel{theta_del_e}{{A.33}{A-20}}
\newlabel{atilde2}{{A.34}{A-21}}
\newlabel{eqs}{{A.35}{A-22}}
\newlabel{three_integrals}{{A.36}{A-23}}
\newlabel{cv14}{{A.37}{A-23}}
\newlabel{cv6}{{A.38}{A-23}}
\newlabel{cv5}{{A.39}{A-23}}
\newlabel{decomp}{{A.40}{A-23}}
\newlabel{cv15}{{A.41}{A-24}}
\newlabel{c*tilde0}{{A.42}{A-24}}
\newlabel{eq55}{{A.43}{A-25}}
\newlabel{delta_tilde}{{A.44}{A-26}}
\citation{GMZ}
\citation{Beirlant/Mason:95}
\citation{GMZ}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{B}{Proofs of Auxiliary Results for Lemmas A2(i), Lemma A4(i), and Theorem 1}}{A-27}}
\newlabel{appendix:C}{{B}{A-27}}
\citation{Shergin:93}
\newlabel{lem-c1}{{1}{A-28}}
\citation{Abadir:Magnus:05}
\citation{VanDerVaart:98}
\newlabel{eq}{{B.1}{A-29}}
\newlabel{lem-c2}{{2}{A-29}}
\citation{Durrett:10}
\citation{Durrett:10}
\newlabel{eq5}{{B.2}{A-31}}
\newlabel{cv12}{{B.3}{A-31}}
\newlabel{cv25}{{B.4}{A-31}}
\newlabel{cv67}{{B.5}{A-31}}
\newlabel{cv88}{{B.6}{A-32}}
\newlabel{cv54}{{B.7}{A-32}}
\citation{Beirlant/Mason:95}
\citation{Beirlant/Mason:95}
\newlabel{lem-c3}{{3}{A-33}}
\newlabel{bds}{{B.8}{A-33}}
\citation{GMZ}
\citation{GMZ}
\citation{Beirlant/Mason:95}
\citation{GMZ}
\citation{GMZ}
\citation{Feller:66}
\newlabel{cv44}{{B.9}{A-34}}
\newlabel{cv23}{{B.10}{A-35}}
\citation{LSW}
\newlabel{lem-c4}{{4}{A-36}}
\newlabel{lem-c5}{{5}{A-36}}
\newlabel{bd52}{{B.11}{A-36}}
\citation{GMZ}
\newlabel{ineqs}{{B.12}{A-37}}
\newlabel{bdd}{{B.13}{A-37}}
\newlabel{C}{{B.14}{A-37}}
\newlabel{s2}{{B.15}{A-38}}
\newlabel{lem-c6}{{6}{A-38}}
\newlabel{Ce}{{B.16}{A-39}}
\newlabel{Ws}{{B.17}{A-39}}
\citation{Magnus:Neudecker:01}
\newlabel{lambda_t}{{B.18}{A-40}}
\newlabel{lb2}{{B.19}{A-40}}
\citation{Sweeting:77}
\citation{Sweeting:77}
\newlabel{bd35}{{B.20}{A-41}}
\newlabel{trace}{{B.21}{A-41}}
\newlabel{der5}{{B.22}{A-41}}
\newlabel{cv4}{{B.23}{A-42}}
\newlabel{ineq44}{{B.24}{A-42}}
\citation{LSW}
\citation{Horvath:91}
\newlabel{lem-c7}{{7}{A-45}}
\newlabel{dec55}{{B.25}{A-45}}
\newlabel{ineq3}{{B.26}{A-46}}
\newlabel{dec22}{{B.27}{A-46}}
\citation{Horvath:91}
\citation{Horvath:91}
\newlabel{lb}{{B.28}{A-47}}
\newlabel{arg1}{{B.29}{A-47}}
\newlabel{arg2}{{B.30}{A-47}}
\newlabel{arg3}{{B.31}{A-48}}
\newlabel{lem-c8}{{8}{A-50}}
\newlabel{dev7}{{B.32}{A-52}}
\newlabel{LB2}{{B.33}{A-52}}
\citation{Sweeting:77}
\newlabel{var}{{B.34}{A-53}}
\newlabel{bd45}{{B.35}{A-54}}
\newlabel{bd56}{{B.36}{A-54}}
\newlabel{dev67}{{B.37}{A-54}}
\citation{Mason/Polonik:09}
\citation{LSW}
\citation{Shergin:93}
\newlabel{conv_y}{{B.38}{A-55}}
\citation{Shergin:93}
\newlabel{lem-c9}{{9}{A-56}}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{C}{Proofs of Auxiliary Results for Lemmas A2(ii), Lemma A4(ii), and Theorem 1}}{A-56}}
\newlabel{appendix:D}{{C}{A-56}}
\newlabel{lem-d3}{{3}{A-57}}
\newlabel{lem-d4}{{4}{A-58}}
\newlabel{lem-d5}{{5}{A-59}}
\newlabel{bd11}{{C.1}{A-59}}
\newlabel{bds22}{{C.2}{A-59}}
\citation{GMZ}
\newlabel{C*}{{C.3}{A-60}}
\newlabel{sigma_tilde}{{C.4}{A-60}}
\newlabel{lem-d6}{{6}{A-60}}
\newlabel{lambda_b}{{C.5}{A-61}}
\newlabel{lambda_min_b}{{C.6}{A-61}}
\citation{Sweeting:77}
\newlabel{bd0}{{C.7}{A-63}}
\newlabel{bdd3}{{C.8}{A-64}}
\newlabel{lem-d7}{{7}{A-64}}
\citation{Horvath:91}
\newlabel{dev4}{{C.9}{A-66}}
\newlabel{lem-d8}{{8}{A-67}}
\newlabel{dev6}{{C.10}{A-68}}
\newlabel{ineq37}{{C.11}{A-69}}
\newlabel{lb3}{{C.12}{A-69}}
\citation{Sweeting:77}
\newlabel{cv11}{{C.13}{A-70}}
\newlabel{varvar}{{C.14}{A-70}}
\citation{LSW}
\citation{Shergin:93}
\citation{Shergin:93}
\newlabel{conv_y2}{{C.15}{A-72}}
\newlabel{lem-d9}{{9}{A-72}}
\newlabel{lem-d10}{{10}{A-73}}
\newlabel{SIGMA}{{C.16}{A-73}}
\newlabel{ineqs4}{{C.17}{A-74}}
\newlabel{lem-d11}{{11}{A-74}}
\newlabel{lem-d12}{{12}{A-75}}
\citation{Sweeting:77}
\newlabel{convs2}{{C.18}{A-76}}
\newlabel{rate}{{C.19}{A-76}}
\newlabel{bdd4}{{C.20}{A-76}}
\citation{LSW-quantile:15}
\citation{LSW-quantile:15}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{D}{Proof of Theorem AUC1\hbox {}}}{A-77}}
\newlabel{sec:appendix-D}{{D}{A-77}}
\newlabel{error}{{D.1}{A-77}}
\citation{LSW-quantile:15}
\newlabel{develop}{{D.2}{A-78}}
\citation{Tamer:03}
\citation{Andrews/Berry/Jia:04}
\citation{Berry/Tamer:07}
\citation{Aradillas-Lopez/Tamer:08}
\citation{Ciliberto/Tamer:09}
\citation{Beresteanu/Molchanov/Molinari:11}
\citation{Galichon/Henry:11}
\citation{Cheser/Rosen:12}
\citation{Aradillas-Lopez/Rosen:13}
\citation{dePaula:13}
\citation{Blundell/Browning/Crawford:08}
\citation{Blundell/Kristensen/Matzkin:11}
\citation{Hoderlein:Stoye:13}
\citation{Kitamura:Stoye:13}
\citation{Imbens/Manski:04}
\citation{Manski:03}
\citation{Manski:07}
\citation{Manski/Pepper:00}
\citation{Tamer:10}
\citation{Cheser/Rosen:13}
\bibstyle{econometrica}
\bibdata{LSW_23June2017}
\harvardcite{Abadir:Magnus:05}{Abadir and Magnus}{Abadir and Magnus}{2005}
\harvardcite{Andrews/Berry/Jia:04}{Andrews, Berry, and Jia}{Andrews, Berry, and Jia}{2004}
\harvardcite{Aradillas-Lopez/Rosen:13}{Aradillas-L\'{o}pez and Rosen}{Aradillas-L\'{o}pez and Rosen}{2013}
\harvardcite{Aradillas-Lopez/Tamer:08}{Aradillas-L\'{o}pez and Tamer}{Aradillas-L\'{o}pez and Tamer}{2008}
\harvardcite{Beirlant/Mason:95}{Beirlant and Mason}{Beirlant and Mason}{1995}
\harvardcite{Beresteanu/Molchanov/Molinari:11}{Beresteanu, Molchanov, and Molinari}{Beresteanu, Molchanov, and Molinari}{2011}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{E}{Potential Areas of Applications}}{A-79}}
\newlabel{sec:app:literature}{{E}{A-79}}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{}{References}}{A-79}}
\harvardcite{Berry/Tamer:07}{Berry and Tamer}{Berry and Tamer}{2007}
\harvardcite{Blundell/Browning/Crawford:08}{Blundell, Browning, and Crawford}{Blundell, Browning, and Crawford}{2008}
\harvardcite{Blundell/Kristensen/Matzkin:11}{Blundell, Kristensen, and Matzkin}{Blundell, Kristensen, and Matzkin}{2014}
\harvardcite{Chen/Linton/VanKeilegom:03}{Chen, Linton, and Van~Keilegom}{Chen, Linton, and Van~Keilegom}{2003}
\harvardcite{Cheser/Rosen:12}{Chesher and Rosen}{Chesher and Rosen}{2012}
\harvardcite{Cheser/Rosen:13}{Chesher and Rosen}{Chesher and Rosen}{2017}
\harvardcite{Ciliberto/Tamer:09}{Ciliberto and Tamer}{Ciliberto and Tamer}{2009}
\harvardcite{dePaula:13}{de~Paula}{de~Paula}{2013}
\harvardcite{Durrett:10}{Durrett}{Durrett}{2010}
\harvardcite{Feller:66}{Feller}{Feller}{1966}
\harvardcite{Galichon/Henry:11}{Galichon and Henry}{Galichon and Henry}{2011}
\harvardcite{Gine:97}{Gin\'{e}}{Gin\'{e}}{1997}
\harvardcite{GMZ}{Gin\'{e}, Mason, and Zaitsev}{Gin\'{e}, Mason, and Zaitsev}{2003}
\harvardcite{Gine/Zinn:90}{Gin\'{e} and Zinn}{Gin\'{e} and Zinn}{1990}
\harvardcite{Hoderlein:Stoye:13}{Hoderlein and Stoye}{Hoderlein and Stoye}{2014}
\harvardcite{Horvath:91}{Horv\'{a}th}{Horv\'{a}th}{1991}
\harvardcite{Imbens/Manski:04}{Imbens and Manski}{Imbens and Manski}{2004}
\harvardcite{Kitamura:Stoye:13}{Kitamura and Stoye}{Kitamura and Stoye}{2013}
\harvardcite{LSW}{Lee, Song, and Whang}{Lee, Song, and Whang}{2013}
\harvardcite{LSW-quantile:15}{Lee, Song, and Whang}{Lee, Song, and Whang}{2015}
\harvardcite{Linton/Song/Whang:10}{Linton, Song, and Whang}{Linton, Song, and Whang}{2010}
\harvardcite{Magnus:Neudecker:01}{Magnus and Neudecker}{Magnus and Neudecker}{2001}
\harvardcite{Manski:03}{Manski}{Manski}{2003}
\harvardcite{Manski:07}{Manski}{Manski}{2007}
\harvardcite{Manski/Pepper:00}{Manski and Pepper}{Manski and Pepper}{2000}
\harvardcite{Mason/Polonik:09}{Mason and Polonik}{Mason and Polonik}{2009}
\harvardcite{Massart:07}{Massart}{Massart}{2007}
\harvardcite{Shergin:93}{Shergin}{Shergin}{1993}
\harvardcite{Sweeting:77}{Sweeting}{Sweeting}{1977}
\harvardcite{Tamer:03}{Tamer}{Tamer}{2003}
\harvardcite{Tamer:10}{Tamer}{Tamer}{{2010}}
\harvardcite{VanDerVaart:98}{van~der Vaart}{van~der Vaart}{1998}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{68.86317pt}
\newlabel{tocindent1}{77.8367pt}
\newlabel{tocindent2}{34.5pt}
\newlabel{tocindent3}{0pt}