Summary
This paper is concerned with the rate of convergence to zero of theL pmetricsΔ np1≦p≦∞, constructed out of differences between distribution functions, for departure from normality for normed sums of independent and identically distributed random variables with zero mean and unit variance. It is shown that theΔ np are, under broad conditions, asymptotically equivalent in the strong sense that, for 1≦p, p′≦∞,Δ np′/Δnp is universally bounded away from zero and infinity asn→∞.
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Heyde, C.C., Nakata, T. On the asymptotic equivalence ofL pmetrics for convergence to normality. Z. Wahrscheinlichkeitstheorie verw Gebiete 68, 97–106 (1984). https://doi.org/10.1007/BF00535176
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DOI: https://doi.org/10.1007/BF00535176