Mathematics – Probability
Scientific paper
2004-10-06
Annals of Probability 2004, Vol. 32, No. 2, 1419-1437
Mathematics
Probability
Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imsta
Scientific paper
10.1214/009117904000000252
The leading term in the normal approximation to the distribution of Student's t statistic is derived in a general setting, with the sole assumption being that the sampled distribution is in the domain of attraction of a normal law. The form of the leading term is shown to have its origin in the way in which extreme data influence properties of the Studentized sum. The leading-term approximation is used to give the exact rate of convergence in the central limit theorem up to order n^{-1/2}, where n denotes sample size. It is proved that the exact rate uniformly on the whole real line is identical to the exact rate on sets of just three points. Moreover, the exact rate is identical to that for the non-Studentized sum when the latter is normalized for scale using a truncated form of variance, but when the corresponding truncated centering constant is omitted. Examples of characterizations of convergence rates are also given. It is shown that, in some instances, their validity uniformly on the whole real line is equivalent to their validity on just two symmetric points.
Hall Peter
Wang Qiying
No associations
LandOfFree
Exact convergence rate and leading term in central limit theorem for student's t statistic does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Exact convergence rate and leading term in central limit theorem for student's t statistic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exact convergence rate and leading term in central limit theorem for student's t statistic will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-171165