# Uniform and nonuniform estimates in the CLT for Banach valued dependent random variables

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### Cites background from "Uniform and nonuniform estimates in..."

...Since λi,ρ(Ti) is small and u ∆ i (1) depends on Y−i only through the within group proportion 1 Ns−1 ∑ i∈Ns\{i} Yi, this difference becomes negligible by Assumptions 1 and 2....

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...3) 1 {Yi = 1} ≤ 1 { Eyi [ ui (1)|Ti ] ≥ 0 } ....

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...Then ei,U is close to the difference between P{Eyi [ui (1)|Ti] ≥ 0|Xi} and P{ui (1) ≥ −λi,ρ(Ti)|Y−i, Xi}....

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...Then ei,U is close to the difference between P{Eyi [u∆i (1)|Ti] ≥ 0|Xi} and P{u∆i (1) ≥ −λi,ρ(Ti)|Y−i, Xi}....

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...5) 1− πi,L ≤ P {Yi = 1|Xi} ≤ πi,U , where πi,U ≡ P { Eyi [ ui (1)|Ti ] ≥ 0|Xi } and πi,L ≡ P { Eyi [ ui (1)|Ti ] ≤ 0|Xi } ....

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### Cites background from "Uniform and nonuniform estimates in..."

...Certain martingale difference sequences in Banach spaces have been investigated in [1], [10]....

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