On discrete Epanechnikov kernel functions

Chi Yang Chu, Daniel J. Henderson, Christopher Parmeter

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Least-squares cross-validation is commonly used for selection of smoothing parameters in the discrete data setting; however, in many applied situations, it tends to select relatively small bandwidths. This tendency to undersmooth is due in part to the geometric weighting scheme that many discrete kernels possess. This problem may be avoided by using alternative kernel functions. Specifically, discrete versions (both unordered and ordered) of the popular Epanechnikov kernel do not have rapidly decaying weights. The analytic properties of these kernels are contrasted with commonly used discrete kernel functions and their relative performance is compared using both simulated and real data. The simulation and empirical results show that these kernel functions generally perform well and in some cases demonstrate substantial gains in terms of mean squared error.

Original languageEnglish (US)
Pages (from-to)79-105
Number of pages27
JournalComputational Statistics and Data Analysis
Volume116
DOIs
StatePublished - Dec 1 2017

Fingerprint

Kernel Function
kernel
Discrete Data
Unordered
Smoothing Parameter
Mean Squared Error
Cross-validation
Weighting
Least Squares
Bandwidth
Tend
Alternatives
Demonstrate
Simulation

Keywords

  • Cross-validation
  • Discrete kernel
  • Panel data
  • Smoothing

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

On discrete Epanechnikov kernel functions. / Chu, Chi Yang; Henderson, Daniel J.; Parmeter, Christopher.

In: Computational Statistics and Data Analysis, Vol. 116, 01.12.2017, p. 79-105.

Research output: Contribution to journalArticle

Chu, Chi Yang ; Henderson, Daniel J. ; Parmeter, Christopher. / On discrete Epanechnikov kernel functions. In: Computational Statistics and Data Analysis. 2017 ; Vol. 116. pp. 79-105.
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