  Computing the {\em matching statistics} of a string $P[1..m]$ with respect to
a text $T[1..n]$ is a fundamental problem which has application to genome
sequence comparison. In this paper, we study the problem of computing the
matching statistics upon highly repetitive texts. We design three different
data structures that are similar to LZ-compressed indexes. The space costs of
all of them can be measured by $\gamma$, the size of the smallest string
attractor [STOC'2018] and $\delta$, a better measure of repetitiveness
[LATIN'2020].
