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Kernel Density Estimation

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What is Kernel Density Estimation?

In non parametric statistics, a kernel is a type of weighting function used for estimating probability density functions. You can think of it as a function that spread’s a data point’s influence around the point’s close vicinity.

Kernel density estimation extrapolates data to an estimated population probability density function. It’s called “kernel” density estimation because each data point is replaced with a kernel for a distribution; the derived pdf is a sum of all of the individual kernels. One way to think of this is as a general histogram; The area under a histogram is 100% (i.e. it has a total probability of one), so tracing the outline of a histogram gives you a rough pdf (Pruim, 2011). The main difference between the two is that in histograms, you specify the number of bins; for kernel densities, you specify a width (Stata).
kernel density estimation

Why Would I Use a Kernel Density Estimate?

Kernel estimations (and their close cousins, histograms) are arguably a better choice than cumulative distributions for showing up central tendencies like multimodality (Hart et al.).

Kernels are very useful for specific types of density estimation, usually for those types that are difficult to estimate without use of a kernel. For example, circular data can be modeled with the von Mises distribution—a circular analogue of the normal distribution. A von Mises density kernel has two attractive properties: it is symmetric, and decreases with increasing distance from the kernel’s central point (Pewsky et al. 2013). Other common types of kernel functions include:

  • Cosine,
  • Gaussian,
  • Epanechnikov,
  • Parzen,
  • Quadratic,
  • Quartic (biweight),
  • Triangle,
  • Tricube,
  • Triweight,
  • Uniform.

References

Hart, J. et al. Kernel Testing as an Alternative to χ2 Analysis for
Investigating the Distribution of Quantitative Traits. 2009. Retrieved June 15, 2020 from: http://www.stat.tamu.edu/~hart/compare.pdf
Pruim, R. Foundations and Applications of Statistics: An Introduction Using R. American Mathematical Society. 2011.
Stata. Kdensity.


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Stephanie Glen. "Kernel Density Estimation" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/kernel-density-estimation/
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