Nonparametric Estimation of the Underlying Distribution of Binned Continuous Data

TL;DR

This paper introduces a flexible non-parametric method using cubic spline interpolation for estimating distributions from binned data, outperforming traditional heuristics and providing meaningful insights in real-world applications.

Contribution

It presents a novel spline-based approach for non-parametric density estimation from grouped data, improving accuracy over existing heuristic methods.

Findings

Outperforms common heuristic methods in simulations

Provides meaningful estimates in real-world datasets

Identifies some questionable results in practical applications

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.