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Mathematics > Probability

arXiv:1812.08619 (math)
[Submitted on 20 Dec 2018]

Title:Limitations Of Richardson Extrapolation For Kernel Density Estimation

Authors:Ruben G. Ascoli
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Abstract:This paper develops the process of using Richardson Extrapolation to improve the Kernel Density Estimation method, resulting in a more accurate (lower Mean Squared Error) estimate of a probability density function for a distribution of data in $R_d$ given a set of data from the distribution. The method of Richardson Extrapolation is explained, showing how to fix conditioning issues that arise with higher-order extrapolations. Then, it is shown why higher-order estimators do not always provide the best estimate, and it is discussed how to choose the optimal order of the estimate. It is shown that given n one-dimensional data points, it is possible to estimate the probability density function with a mean squared error value on the order of only $n^{-1}\sqrt{\ln(n)}$. Finally, this paper introduces a possible direction of future research that could further minimize the mean squared error.
Comments: 14 pages, 3 figures
Subjects: Probability (math.PR)
MSC classes: 62G07
Cite as: arXiv:1812.08619 [math.PR]
  (or arXiv:1812.08619v1 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.08619

Submission history

From: Ruben Ascoli [view email]
[v1] Thu, 20 Dec 2018 14:58:56 UTC (550 KB)
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