DENSITY-ESTIMATION WITH NONPARAMETRIC METHODS

One key issue in several astrophysical problems is the evaluation of t he density probability function underlying an observational discrete d ata set. We here review two non-parametric density estimators which re cently appeared in the astrophysical literature, namely the adaptive k ernel density estimator and the Maximum Penalized Likelihood technique , and describe another method based on the wavelet transform. The effi ciency of these estimators is tested by using extensive numerical simu lations in the one-dimensional case. The results are in good agreement with theoretical functions and the three methods appear to yield cons istent estimates. However! the Maximum Penalized Likelihood suffers fr om a lack of resolution and high computational cost due to its depende ncy on a minimization algorithm. The small differences between kernel and wavelet estimates are mainly explained by the ability of the wavel et method to take into account local gaps in the data distribution. Th is new approach is very promising, since smaller structures superimpos ed onto a larger one are detected only by this technique, especially w hen small samples are investigated. Thus, wavelet solutions appear to be better suited for subclustering studies. Nevertheless, kernel estim ates seem more robust and are reliable solutions although some small-s cale details can be missed. In order to check these estimators with re spect to previous studies, two galaxy redshift samples, related to the galaxy cluster A3526 and to the Corona Borealis region, have been ana lyzed. In both these cases claims for bimodality are confirmed at a hi gh confidence level.