Recent content by JanO

It seems like bounded here means all most surely bounded. At least that's how Hoeffding inequality seems to be given elsewhere. I guess it then means that z=\bar{x}-\bar{y} is bounded a.s. between [\mu_x-\mu_y-\frac{1}{2}\sqrt{m^{-1}+n^{-1}}, \ \mu_x-\mu_y+\frac{1}{2}\sqrt{m^{-1}+n^{-1}}]...

Thanks Chiro for your responce. However, I still do not understand how the term (m^{-1} + n^{-1}) comes into the bound. Isn't z=\bar{x}-\bar{y} is still bounded between [0,1]? -Jan

In W. Hoeffding's 1963 paper* he gives the well known inequality: P(\bar{x}-\mathrm{E}[x_i] \geq t) \leq \exp(-2t^2n) \ \ \ \ \ \ (1), where \bar{x} = \frac{1}{n}\sum_{i=1}^nx_i, x_i\in[0,1]. x_i's are independent. Following this theorem he gives a corollary for the difference of two...