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- W2034783777 abstract "Abstract Let { ξ 1 , ξ 2 , … , ξ n } be a sequence of independent and identically distributed U[0,1]-distributed random variables. Define the uniform empirical process F n ( t ) = n − 1 2 ∑ i = 1 n ( I { ξ i ≤ t } − t ) , 0 ≤ t ≤ 1 , ‖ F n ‖ = sup 0 ≤ t ≤ 1 | F n ( t ) | . For 1 ≤ p 2 , a n = O ( 1 / log log n ) , we have the limits of weighted infinite series of P { ‖ F n ‖ ≥ e n 1 / p − 1 / 2 } , P { ‖ F n ‖ ≥ e log n } and P { ‖ F n ‖ ≥ ( e + a n ) 2 log log n } as e → 0 ." @default.
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- W2034783777 date "2008-07-01" @default.
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- W2034783777 title "Precise asymptotics in the law of the iterated logarithm and the complete convergence for uniform empirical process" @default.
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- W2034783777 doi "https://doi.org/10.1016/j.spl.2007.09.063" @default.
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