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.
CITATION STYLE
Dickhaus, T., & Finner, H. (2016). Asymptotic density crossing points of self-normalized sums and normal. In Springer Proceedings in Mathematics and Statistics (Vol. 124, pp. 199–209). Springer New York LLC. https://doi.org/10.5176/2251-1911_CMCGS14.02_17
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