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Tightness of the Student $t$-Statistic

   
@article{ECP1059,
	author = {Philip Griffin},
	title = {Tightness of the Student $t$-Statistic},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {7},
	year = {2002},
	keywords = {tightness, t-statistic, self-normalized sum},
	abstract = {Let $X, X_1, X_2, \dots $ be a sequence of nondegenerate, independent and identically distributed random variables and set $S_n=X_1+\dots +X_n$,  $V_n^2=X_1^2+\dots +X_n^2$. We answer a question of Gotze, Gine and Mason by providing a simple necessary and sufficient condition for tightness of $S_n/V_n$.},
	pages = {no. 18, 181-190},
	issn = {1083-589X},
	doi = {10.1214/ECP.v7-1059},    
        url = {http://ecp.ejpecp.org/article/view/1059}}