Bootstrapping the Student t‐Statistic
Document Type
Lecture
Publication Date
4-29-2016
Abstract
Let ��₁, …, ��ₙ, with n ≥ 2, be independent identically distributed random variables (r.v.s) and consider the Student t-statistic ��ₙ based on these r.v.s. Giné, Goetze, and Mason (1997) proved that ��ₙ converges in distribution to a standard normal r.v. if and only if �� is in the domain of attraction of a normal r.v. and ��[��] = 0. We shall show that roughly the same holds true for the bootstrapped Student t-statistics ��ₙ. In the process, we shall disclose all of the possible subsequential limit laws of ��ₙ. The proofs introduce a number of amusing tricks that may be of independent interest. A conjecture related to a result of Peter Hall (1990) is posed. This talk is based on work by Mason and Q.-M. Shao (2001).
Relational Format
presentation
Recommended Citation
Mason, David, "Bootstrapping the Student t‐Statistic" (2016). Probability & Statistics Seminar. 36.
https://egrove.olemiss.edu/math_statistics/36
