When is the student t-statistic asymptotically standard normal?
Gine, E
Gine
E
Götze, Friedrich
Götze
Friedrich
Mason, DM
Mason
DM
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.
25
3
1514-1531
1514-1531
INST MATHEMATICAL STATISTICS
1997