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- W2061284139 abstract "Let $S_n$ denote the $n$th partial sum of i.i.d. nonconstant mean zero random variables. Given an approximation $K(n)$ of $E|S_n|$, tight bounds are obtained for the ratio $E|S_n|/K(n)$. These bounds are best possible as $n$ tends to infinity. Implications of this result relate to the law of the iterated logarithm for mean zero variables, Chebyshev's inequality and Markov's inequality. Asymptotically exact lower-bounds are obtained for expectations of functions of row-sums of triangular arrays of independent but not necessarily identically distributed random variables. Expectations of Poissonized random sums are also treated." @default.
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- W2061284139 date "1980-04-01" @default.
- W2061284139 modified "2023-09-24" @default.
- W2061284139 title "Precision Bounds for the Relative Error in the Approximation of $E|S_n|$ and Extensions" @default.
- W2061284139 doi "https://doi.org/10.1214/aop/1176994782" @default.
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