A sharpening of Tusnády's inequality

Details A sharpening of Tusnády's inequality A sharpening of Tusnády's inequality

2011-10-17

arxiv.org/abs/1110.3627v3

Mathematics

Statistics Theory

7 pages and 2 figures in pdf files

Scientific paper

Let ~$\veps_1, ..., \veps_m$ be i.i.d. random variables with $$P(\veps_i=1)= P(\veps_i= -1)=1/2,$$ and $X_m = \sum_{i=1}^m \veps_i.$ Let $Y_m $ be a normal random variable with the same first two moments as that of $X_m.$ There is a uniquely determined function $\Psi_m$ such that the distribution of $\Psi_m(Y_m)$ equals to the distribution of $X_m$. Tusn\'ady's inequality states that $$ \mid \Psi_m(Y_m) - Y_m \mid \leq \frac{Y_m^2}{m}+1.$$ Here we propose a sharpened version of this inequality.

Affiliated with

Also associated with

No associations

Rating

A sharpening of Tusnády's inequality 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 A sharpening of Tusnády's inequality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A sharpening of Tusnády's inequality will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-317602