On $L_p$ Chebyshev-Cramer Asymptotic Expansions

R. V. Erickson

doi:10.1214/aop/1176996993

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Home > Journals > Ann. Probab. > Volume 1 > Issue 2 > Article

April, 1973 On $L_p$ Chebyshev-Cramer Asymptotic Expansions

R. V. Erickson

Ann. Probab. 1(2): 355-361 (April, 1973). DOI: 10.1214/aop/1176996993

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Abstract

An $L_1$-smoothing lemma is used to prove an $L_1$ version of the Chebyshev-Cramer asymptotic expansion for independent (identically distributed) random variables. The conditions imposed are exactly those demanded for the $L_\infty$ version.