Nonparametric Estimation of the Underlying Distribution of Binned Continuous Data
Abstract
The estimation of cumulative distribution functions (CDF) and probability density functions (PDF) is a fundamental practice in applied statistics. However, challenges often arise when dealing with data arranged in grouped intervals. In this paper, we discuss a suitable and highly flexible non-parametric density estimation approach for binned distributions, based on cubic monotonicity-preserving splines - known as cubic spline interpolation. Results from simulation studies demonstrate that this approach outperforms many widely used heuristic methods. Additionally, the application of this method to a dataset of train delays in Germany and micro census data on distance and travel time to work yields both meaningful but also some questionable results.
Cite
@article{arxiv.2309.12575,
title = {Nonparametric Estimation of the Underlying Distribution of Binned Continuous Data},
author = {Ejike R. Ugba and Jan Gertheiss},
journal= {arXiv preprint arXiv:2309.12575},
year = {2023}
}