Asymptotic Density Crossing Points of Self-Normalized Sums and Normal
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.
KeywordsEdgeworth expansion Large deviations Likelihood ratio Student’s t
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