Asymptotic Density Crossing Points of Self-Normalized Sums and Normal

  • Thorsten DickhausEmail author
  • Helmut Finner
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 124)


We define generalized self-normalized sums as t-type statistics with flexible norming sequence in the denominator. It will be shown how Edgeworth expansions can be utilized to provide a full characterization of asymptotic crossing points (ACPs) between the density of such generalized self-normalized sums and the standard normal density. Although the proof of our main ACP theorem is self-contained, we also draw connections to related expansions for the cumulative distribution function of generalized self-normalized sums that we have derived in previous work.


Edgeworth expansion Large deviations Likelihood ratio Student’s t 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute for StatisticsUniversity of BremenBremenGermany
  2. 2.Institute of Biometrics and EpidemiologyGerman Diabetes CenterDüsseldorfGermany

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