Estimating the K function of a point process with an application to cosmology

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.