kde: One-dimensional kernel density estimate

Description

State-of-the-art gaussian kernel density estimator for one-dimensional data. The estimator does not use the commonly employed 'gaussian rule of thumb'. As a result, it outperforms many plug-in methods on multimodal densities with widely separated modes. This function is the cleaned-up version of the code written and published by Z. I. Botev at: http://web.maths.unsw.edu.au/~zdravkobotev/

Usage

kde(data, n, MIN, MAX)

Arguments

data

a vector of data from which the density estimate is constructed;

the number of mesh points used in the uniform discretization of the interval [MIN, MAX]; n has to be a power of two; if n is not a power of two, then n is rounded up to the next power of two; the default value of n is n=2 ^ 12;

MIN

minimum of the interval [MIN, MAX] on which the density estimate is constructed; default value: MIN = min(data) - Range / 10

MAX

maximum of the interval [MIN, MAX] on which the density estimate is constructed; default value: MAX = max(data) + Range / 10

Value

A matrix with two rows of length n, where the second row contains the density values on the mesh in the first row.

References

Z. I. Botev, J. F. Grotowski and D. P. Kroese, "Kernel Density Estimation Via Diffusion", Annals of Statistics, 2010, Volume 38, Number 5, Pages 2916-2957

Examples

Run this code

# NOT RUN {
set.seed(1)
data <- c(rnorm(10 ^ 3), rnorm(10 ^ 3) * 2 + 30)
d <- kde(data)
plot(d[1,], d[2,], type = 'l', xlab = 'x', ylab = 'density f(x)')
# }

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