Nonparametric density estimation and clustering in astronomical sky surveys

We present a nonparametric method for galaxy clustering in astronomical sky surveys. We show that the cosmological definition of clusters of galaxies is equivalent to density contour clusters (Hartigan, 1975) Sc={f>c}Sc={f>c} where f   is a probability density function. The plug-in estimator S^c=f^>c is used to estimate ScSc where f^ is the multivariate kernel density estimator. To choose the optimal smoothing parameter, we use cross-validation and the plug-in method and show that cross-validation method outperforms the plug-in method in our case. A new cluster catalog, database of the locations of clusters, based on the plug-in estimator is compared to existing cluster catalogs, the Abell and Edinburgh/Durham Cluster Catalog I (EDCCI). Our result is more consistent with the EDCCI than with the Abell, which is the most widely used catalog. We use the smoothed bootstrap to asses the validity of clustering results.