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Suppose that X1, . . . ,Xn are independent, identically-distributed random variables of mean zero and variance one. Assume that E|X1| ≤ δ4. We observe that there exist many choices of coefficients θ1, . . . , θn ∈ R with ∑ j θ 2 j = 1 for which sup α,β∈R α<β ∣∣∣∣∣ P α ≤ n ∑ j=1 θjXj ≤ β − 1 √ 2π ∫ β α e−t 2/2dt ∣∣∣∣∣ ≤ Cδ 4 n , (1) where C > 0 is a universal constant. Inequality (1) shou...
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ژورنال
عنوان ژورنال: Theory of Probability & Its Applications
سال: 2012
ISSN: 0040-585X,1095-7219
DOI: 10.1137/s0040585x97985522