Motivated by the study of an important data set for understanding
the large-scale structure of the universe, this work considers the estimation
of the reduced second-moment function, or $K$ function, of a stationary point
process on $\mathbb{R}$ observed over a large number of segments of possibly
varying lengths. Theory and simulation are used to compare the behavior of
isotropic and rigid motion correction estimators and some modifications of
these estimators. These results generally support the use of modified versions
of the rigid motion correction.When applied to a catalog of astronomical
objects known as absorbers, the proposed methods confirm results from earlier
analyses of the absorber catalog showing clear evidence of clustering up to $50
h^{-1}$ Mpc and marginal evidence for clustering of matter on spatial scales
beyond $100 h^{-1}$ Mpc, which is beyond the distance at which clustering of
matter is now generally accepted to exist.