  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 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 Mpc and marginal
evidence for clustering of matter on spatial scales beyond 100 Mpc, which is
beyond the distance at which clustering of matter is now generally accepted to
exist.
