On the asymptotic equivalence ofLpmetrics for convergence to normality

  • C. C. Heyde
  • T. Nakata


This paper is concerned with the rate of convergence to zero of theLpmetricsΔnp1≦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 theΔnp are, under broad conditions, asymptotically equivalent in the strong sense that, for 1≦p, p′≦∞,Δnp′np is universally bounded away from zero and infinity asn→∞.


Distribution Function Stochastic Process Probability Theory Mathematical Biology Strong Sense 
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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • C. C. Heyde
    • 1
  • T. Nakata
    • 2
  1. 1.Department of StatisticsUniversity of MelbourneParkvilleAustralia
  2. 2.Chukyo UniversityNagoya CityJapan

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