Authors: Thorsten Dickhaus, and Helmut Finner
Abstract: 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 selfnormalized
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.
Keywords: Edgeworth expansion; large deviations; likelihood ratio; Student’s t