Date of Award
2025-05-01
Degree Name
Master of Science
Department
Mathematical Sciences
Advisor(s)
Xiaogang Su
Abstract
Kernel Density Estimation (KDE) is a widely used technique for estimating the probability density function of a random variable. In this study, we revisit KDE through the lens of convolution and extend this perspective to special cases such as positive, bounded and heavy tailed random variables. Building on this foundation, we propose a novel simulation-based density estimation method that generates new data by adding noise to observed values and then smoothing the resulting histogram using splines. A minor adjustment to natural cubic splines is required to ensure nonnegative estimates. The noise is drawn from a class of bounded polynomial kernel densities obtained via convolution of uniform random variables, with the smoothing parameter naturally defined by the support bound. A practical choice for this parameter is determined by a percentile of the neighboring distances among sorted data. The proposed method offers enhanced flexibility for handling variables with specific support constraints (e.g., positive, bounded and heavy tailed) through simple transformations, and numerical studies demonstrate its competitive or superior performance compared to standard KDE across various scenarios.
Language
en
Provenance
Received from ProQuest
Copyright Date
2025-05
File Size
129 p.
File Format
application/pdf
Rights Holder
Nicholas Tenkorang
Recommended Citation
Tenkorang, Nicholas, "Kernel Density Estimation and Convolution" (2025). Open Access Theses & Dissertations. 4483.
https://scholarworks.utep.edu/open_etd/4483