Improving Radio Source Count Estimation Using Kernel Density Estimation

Abstract

Radio source counts provide a fundamental census of cosmic radio emission, yet their estimation is usually based on coarse histograms that suffer from bin-choice bias, boundary effects, and survey incompleteness. We apply and rigorously evaluate kernel density estimation (KDE) as a anonparametric alternative to the conventional binned method for estimating differential radio source counts. Using simulated flux-limited samples derived from an input luminosity function model, we compare the performance of standard KDE, adaptive KDE, and traditional binning methods. Our results show that KDE-based approaches yield more accurate and stable estimates, particularly in the high-flux regime where data are sparse and conventional methods struggle. We also apply the adaptive KDE method to real observational data from the LOFAR Two-Metre Sky Survey Deep Fields. Our analysis robustly confirms the pronounced ``drop and bump" feature at sub-mJy flux densities, but also reveals that a secondary, modest bump seen in the binned data at ~ $\sim 10$ mJy is likely a binning artifact. We also demonstrate the flexibility of KDE in addressing observational incompleteness through weighted estimation, which applies weights continuously at the level of individual sources rather than averaging them in discrete bins. These strengths make KDE a powerful tool for source-count analyses in current and future radio surveys and, more broadly, in analogous studies at other wavelengths. All computations in this study are implemented with \texttt{AstroKDE}, a Python package we have developed for astronomical applications.