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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
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where b1 and b2 depend only on κ, Ä, a and p̄. As in Zhilova (2015), note that kÆik ai = sup γ∈Rpi :kγk=a−1 i γ0 Æi. We employ an approximation argument based on the inequality P max 1≤i≤N kÆik ai − cN ≤ ≤P max 1≤i≤N max γj∈Γi γ0 jÆi − cN ≤ 2 + P max 1≤i≤N sup γ∈Rpi :kγk=a−1 i min γj∈Γi |(γ − γj)0 Æi| > ! ≡A1 + A2. To bound A1, note that each γ0 jÆi is a normal random variable with standard deviation bounded between ā−1 and a−1. This follows from our assumptions about the covering Γi and E (γ0 jÆi)2 = γ0 jE[ÆiÆ0 i]γj = kγjk2 = a−2 i .
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