Nonparametric Estimation of the Underlying Distribution of Binned Continuous Data

Ejike R. Ugba; Jan Gertheiss

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arXiv · 2309.12575

Nonparametric Estimation of the Underlying Distribution of Binned Continuous Data

Ejike R. Ugba·Jan Gertheiss

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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.

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BibTeX RIS

Ejike R. Ugba, Jan Gertheiss. 2023-09-22. Nonparametric Estimation of the Underlying Distribution of Binned Continuous Data. https://arxiv.org/abs/2309.12575

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