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 proce
ss on R observed over a large number of segments of possibly varying length
s. Theory and simulation are used to compare the behavior of isotropic and
rigid motion correction estimators and some modifications of these estimato
rs. These results generally support the use of modified versions of the rig
id motion correction. When applied to a catalog of astronomical objects kno
wn 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 beyo
nd 100 h(-1) Mpc, which is beyond the distance at which clustering of matte
r is now generally accepted to exist.