When is the student t-statistic asymptotically standard normal?

Gine E, Götze F, Mason DM (1997)
ANNALS OF PROBABILITY 25(3): 1514-1531.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
Let X, X-i, i is an element of N, be independent, identically distributed random variables. It is shown that the Student t-statistic based upon the sample {X-i}(i less than or equal to 1)(n) is asymptotically N(0, 1) if and only if X is in the domain of attraction of the normal law. It is also shown that, for any X, if the self-normalized sums U-n := Sigma(i=1)(n) X-i/(Sigma(i=1)(n) X-i(2))(1/2), n is an element of N, are stochastically bounded then they are uniformly subgaussian that is, sup(n) E exp(lambda U-n(2)) < infinity for some lambda > 0.
Erscheinungsjahr
Zeitschriftentitel
ANNALS OF PROBABILITY
Band
25
Ausgabe
3
Seite(n)
1514-1531
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Gine E, Götze F, Mason DM. When is the student t-statistic asymptotically standard normal? ANNALS OF PROBABILITY. 1997;25(3):1514-1531.
Gine, E., Götze, F., & Mason, D. M. (1997). When is the student t-statistic asymptotically standard normal? ANNALS OF PROBABILITY, 25(3), 1514-1531.
Gine, E., Götze, F., and Mason, D. M. (1997). When is the student t-statistic asymptotically standard normal? ANNALS OF PROBABILITY 25, 1514-1531.
Gine, E., Götze, F., & Mason, D.M., 1997. When is the student t-statistic asymptotically standard normal? ANNALS OF PROBABILITY, 25(3), p 1514-1531.
E. Gine, F. Götze, and D.M. Mason, “When is the student t-statistic asymptotically standard normal?”, ANNALS OF PROBABILITY, vol. 25, 1997, pp. 1514-1531.
Gine, E., Götze, F., Mason, D.M.: When is the student t-statistic asymptotically standard normal? ANNALS OF PROBABILITY. 25, 1514-1531 (1997).
Gine, E, Götze, Friedrich, and Mason, DM. “When is the student t-statistic asymptotically standard normal?”. ANNALS OF PROBABILITY 25.3 (1997): 1514-1531.