= Rejection point of an influence function
{title2=$\rho^*(T,F)$}
For observations expressed in centered, standardized coordinates, the rejection point is
$$
\rho^*(T,F)=\inf\{r\ge0:\operatorname{IF}(x;T,F)=0\text{ whenever }|x|>r\},
$$
with value $\infty$ if the set is empty. A finite rejection point means sufficiently distant contamination has zero first-order effect. Boundedness of the <influence function> does not imply a finite rejection point: the <influence function of a quantile> has nonzero constant tails. Nor does tending to zero at infinity guarantee a finite rejection point unless those tails become identically zero.
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