I am currently reading a paper Zieliński R. Robust statistical procedures: A general approach and I have a few questions:
Function $r_t(P)=\sup\{\rho(Q): Q \in \pi(P)\}-\inf\{\rho(Q): Q \in \pi(P)\}$ is defined as a diameter of a set, so why is there a need to include infimum?
How could one justify forumulas for $r_t^+$ and $r_t^-$? I don't really get what's the reason to define it in this way.
Why could one say that an estimate $t$ is robust at given point $P$ if $\int t(x)dQ= \theta(P)$? How to interpret this integral, as an expected value of a statistic?
A part of an article below:
