Content area

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.

Details

1010268
Title
Kernel Density Estimation and Convolution
Number of pages
130
Publication year
2025
Degree date
2025
School code
0459
Source
MAI 86/12(E), Masters Abstracts International
ISBN
9798315789178
Advisor
Committee member
Wagler, Amy; Chatla, Suneel Babu
University/institution
The University of Texas at El Paso
Department
Mathematical Sciences
University location
United States -- Texas
Degree
M.S.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
32040700
ProQuest document ID
3215569988
Document URL
https://www.proquest.com/dissertations-theses/kernel-density-estimation-convolution/docview/3215569988/se-2?accountid=208611
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Database
ProQuest One Academic