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Andreas, Dzemski ; Ryo, Okui ; Ryo, Okui. (2018) Confidence Set for Group Membership.
In: Working Papers in Economics. RePEc:hhs:gunwpe:0727.
Full description at Econpapers
cites:
Lemma E.1 part (iii) and following the same argument of Lemma A.5 of Chernozhukov, Chetverikov, and Kato (2014). Following the argument in the proof of Step 2 of Theorem 4.2 of Chernozhukov, Chetverikov, and Kato (2014) under (8), (9) and that (10) and (11) implies U N,T,2 p log((G − 1)N/β) ≤ CT−1/6, it holds that P max 1≤i≤N max h∈G\{g(i)} √ T(E( dU i (h)) − dU i (h)) S̃U i,T (h) > (1 − r)cSNS β,N − CU N,T,2 ! ≤ β + CT−c . For the second term (34), let ait(h) = 2(dU it(h)−EP (dU it(h)))(EP (dU it(h))−EP ( dU i (h)))/(ÃisU i,T (h))2. The second term is P max 1≤i≤N max h∈G\{g(i)} 1 T T X t=1 ãit(h) > r 2 − r2 16 ! ≤P max 1≤i≤N max h∈G\{g(i)} 1 T T X t=1 ait(h) > 1 − r 2 r 2 − r2 16 ! + P max 1≤i≤N max h∈G\{g(i)} (S̃U i,T (h))2 (ÃisU i,T (h))2 − 1 > r 2 ! ,
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