On bounds for moderate deviations for Student's statistic

Let $X_1,X_2,\dots$ be independent random variables with zero means and finite variances. In this paper we prove lower bounds for a Cramér-type large deviation theorem for self-normalized sums which imply that the bounds obtained by Jing, Shao, and Wang [Ann. Probab., 31 (2003), pp. 2167–2215] are sharp.