Refined Self-normalized Large Deviations for Independent Random Variables

Let X (1),X (2),......, be independent random variables with EX (i) =0 and write S-n = Sigma(n)(i=1) X-i and V-n(2) = Sigma(n)(i=1) X-i(2). This paper provides new refined results on the Cram,r-type large deviation for the so-called self-normalized sum S (n) /V (n) . The major techniques used to derive these new findings are different from those used previously.