Density estimation with non-parametric methods

One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the astrophysical literature, namely the adaptive kernel density estimator and the Maximum Penalized Likelihood technique, and describe another method based on the wavelet transform. The efficiency of these estimators is tested by using extensive numerical simulations in the one-dimensional case. The results are in good agreement with theoretical functions and the three methods appear to yield consistent estimates. In order to check these estimators with respect to previous studies, two galaxy redshift samples (the galaxy cluster A3526 and the Corona Borealis region) have been analyzed.