On weighted approximations in $D[0,1]$ with applications to self-normalized partial sum processes

Miklós Csörgő, Barbara Szyszkowicz, Qiying Wang

Let $X,X_1,X_2,...$ be a sequence of non-degenerate i.i.d. random variables with mean zero. The best possible weighted approximations are investigated in $D[0,1]$ for the partia…