## 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).

## 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 χ^{2} 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

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