kdeDirichlet {compositions}

Density estimation on the simplex with Dirichlet kernel

Description

Function to compute the kernel density estimation on a grid of the simplex

Usage

kdeDirichlet(x, adj = 1, n = 200, kdegrid = NULL, delta = FALSE)

Arguments

x

data set of (complete) compositional data, i.e. data summing to 1 by columns

adj

accessory scaling factor, for modifying the bandwith in analogy to function [MASS::kde()]

n

integer, number of grid nodes on each component, where to estimate the density; ignored if 'kdegrid' is given

kdegrid

data frame, set of locations where to estimate the density; either specify 'n' or 'kdegrid'

delta

logical or real controlling if/how zeroes in 'x' are treated; logical works only for 'kdegrid=NULL' and uses correction by half the grid cell size, otherwise give a real value; this value will be added to the whole composition, including the non-zero values.

Details

This function computes the kde (kernel density estimation) of the probability density function of a random composition on the simplex, by using Dirichlet kernels. The method was proposed by Aitchison and Lauder (1985).

Value

A list of two or three elements, depending on the value of 'kdegrid'. If 'kdegrid' is null, the function is assumed to be used for two-dimensional plotting, and the output is one compatible with the function [image()], i.e. a list of three elements (vector of x-values, vector of y-values and matrix of density values computed). If 'kdegrid' is a grid, then the output has two elements: the input grid and a vector of computed densities.

NOTE: no effort is made to check that 'kdegrid' has the right class, dimension or content.

References

Aitchison J., Lauder I.J. (1985) Kernel density estimation for compositional data; _J. Roy. Statist. Soc. Ser. C_, 34 (2): 129-137.

Ouimet, F. and Tolosana-Delgado, R. (2022) Asymptotic properties of Dirichlet kernel density estimators; _Journal of Multivariate Analysis_ 187: 104832, doi: 10.1016/j.jmva.2021.104832