Package 'demoKde'

Kernel density estimation demonstration and exploration

Description

Teaching demonstration code for kernel density estimates. KDEs are computed in native R code directly from the definition. The slight innovation here is to replace the observations by their frequencies in a fine partition of the range of the sample. Kernels may be supplied as a function in a standard form, thus allowing alternative kernel functions to be devised and empirically investigated. A wide selection of kernel function is also provided with the package. The canonical reference is B. W. Silverman, (1998). See Refrences.

Author(s)

Bill Venables

Maintainer: Bill Venables, <[email protected]>

References

See https://en.wikipedia.org/wiki/Kernel_(statistics) for details of the kernel functions. See also B. W. Silverman, (1998) Density Estimation for Statistics and Data Analysis. Taylor & Franis Group, Boca Raton. doi:10.1201/9781315140919.

See Also

density

Examples

if(require("graphics")) {
  with(MASS::Boston, {
      Criminality <- log(crim)
      hist(Criminality, freq=FALSE, main="", border="grey", las=1)
      lines(stats::density(Criminality), col="skyblue", lwd=8)
      lines(kde(Criminality))
      lines(kde(Criminality, kernel = kernelUniform), col="red")
      rug(jitter(Criminality), col="blue")
      legend("topright", c("density histogram",
        "KDE gaussian (denstiy)", "KDE gaussian (kde)",
        "KDE rectangular (kde)"), lty = "solid", lwd=c(1,8,1,1),
        col=c("grey", "skyblue", "black", "red"), bty="n")
  })
}

---

Univariate kernel density estimation directly in R code.

Description

This function behaves similarly to the density function of the stats package, but uses only R code. It is a demonstration function intended to show how kernel density estimates are computed, at least conceptually. Unlike density, the kernel may be supplied as an R function in a standard form. Example kernel functions are provided. For computational efficiency, the density function of the stats package is far superior.

Usage

kde(x, bw = bw.nrd0, kernel = kernelGaussian, n = 512,
    from = min(x) - cut * sd, to = max(x) + cut * sd,
    adjust = 1, cut = 3, ...)

Arguments

x	Univeriate sample. Must be numeric.
bw	Either an explicit numeric bandwidth to be used for the kernel, or a function used to calculate it.
kernel	The kernel function to be used. Must have the same argument sequence as kernelGaussian, with the same meanings.
n	Then number of points covering the range at which to evaluate the KDE. More gives a smoother display of the result; fewer gives a quicker and more memory efficient computation.
from	Lower boundary for the computed KDE.
to	Upper boundary for the computed KDE.
adjust	Adjustment factor to be used for the bandwidth.
cut	Number of bandwidths by which to extend the range of the data for the range of the KDE
...	Additional arguments, if needed, to be supplied to the kernel function.

Details

This is a demonstration function intended to show, via R code, the way in which a kernel density estimate is computed.

For samples which are not too large the computation is reasonably efficient, but for serious computations the standard function density, or some alternative, should be used.

Value

An object of class “density”, with essentially the same structure as objects generated by the density of the stats package. plot and allied methods should apply.

Note

Demonstration code only!

Author(s)

Bill Venables

See Also

kernelBiweight and aliases; density.

Examples

if(require("graphics")) {
  with(MASS::geyser, {
      hist(waiting, freq=FALSE, main="", border="grey", las=1)
      lines(stats::density(waiting), col="skyblue", lwd=8)
      lines(kde(waiting))
      lines(kde(waiting, kernel = kernelUniform), col="red")
      rug(jitter(waiting), col="blue")
      legend("topleft", c("density histogram",
        "KDE gaussian (denstiy)", "KDE gaussian (kde)",
        "KDE rectangular (kde)"), lty = "solid", lwd=c(1,8,1,1),
        col=c("grey", "skyblue", "black", "red"), bty="n")
  })
}

---

Kernel functions for use with kde

Description

These functions, all with idenical argument lists, provide kernel functions for use with the KDE function.

Usage

kernelBiweight(x, mean = 0, sd = 1)
kernelCosine(x, mean = 0, sd = 1)
kernelEpanechnikov(x, mean = 0, sd = 1)
kernelGaussian(x, mean = 0, sd = 1)
kernelLogistic(x, mean = 0, sd = 1)
kernelOptCosine(x, mean = 0, sd = 1)
kernelRectangular(x, mean = 0, sd = 1)
kernelSquaredCosine(x, mean = 0, sd = 1)
kernelTriangular(x, mean = 0, sd = 1)
kernelTricube(x, mean = 0, sd = 1)
kernelTriweight(x, mean = 0, sd = 1)
kernelUniform(x, mean = 0, sd = 1)

Arguments

x	Values for which the kernel function is to be evaluated.
mean	Mean (or location parameter) of the kernel function.
sd	Standard deviation (or scale paramenter) of the kernel function.

Details

These are all continuous, symmetric probability density functions parametrised by a location and scale parameter, here taken to be the mean and standard deviation respectively. Most have finite support, he two exceptions here being kernelGaussian and kernelLogistic, which have unbounded support.

The functions provided cover all those listed in https://en.wikipedia.org/wiki/Kernel_(statistics), with obvious name correspondences. Of the additional ones, kernelSquaredCosine appears to be thus far new, and kernelOptCosine is explained in the help file for stats::density.

The functions kernelUniform and kernelRectangular are identical, and provided for convenience.

The functions are vectorized with respect to all three parameters.

Value

The evaluated kernel for each supplied x value.

Author(s)

Bill Venables

References

See this web site, primarily.

See Also

kde, density

Examples

if(require("graphics")) {
  curve(kernelGaussian, xlim = c(-4.5, 4.5), ylim = c(0, 0.45))
  curve(kernelLogistic, add = TRUE, col = "red")
  curve(kernelUniform, add = TRUE, col = "blue", lwd=2, n = 5000)
}

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