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

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

2007-11-09

arxiv.org/abs/0711.1384v1

Mathematics

Probability

22 pages

Scientific paper

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 partial sum processes $\{S_{[nt]}, 0\le t\le 1\}$, where $S_n=\sum_{j=1}^nX_j$, under the assumption that $X$ belongs to the domain of attraction of the normal law. The conclusions then are used to establish similar results for the sequence of self-normalized partial sum processes $\{S_{[nt]}/V_n, 0\le t\le 1\}$, where $V_n^2=\sum_{j=1}^nX_j^2$. $L_p$ approximations of self-normalized partial sum processes are also discussed.

Affiliated with

Also associated with

No associations

Rating

On weighted approximations in $D[0, 1]$ with applications to self-normalized partial sum processes 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 On weighted approximations in $D[0, 1]$ with applications to self-normalized partial sum processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On weighted approximations in $D[0, 1]$ with applications to self-normalized partial sum processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-701775