gplm (version 0.7-4)

kernel.function: Kernel function

Description

Calculates several kernel functions (uniform, triangle, epanechnikov, biweight, triweight, gaussian).

Usage

kernel.function(u, kernel = "biweight", product = TRUE)

Arguments

u

n x d matrix

kernel

text string

product

(if d>1) product or spherical kernel

Value

n x 1 vector of kernel weights

Details

The kernel parameter is a text string specifying the univariate kernel function which is either the gaussian pdf or proportional to $(1-|u|^p)^q$. Possible text strings are "triangle" (p=q=1), "uniform" (p=1, q=0), "epanechnikov" (p=2, q=1), "biweight" or "quartic" (p=q=2), "triweight" (p=2, q=3), "gaussian" or "normal" (gaussian pdf).

The multivariate kernels are obtained by a product of unvariate kernels $K(u_1)...K(u_d)$ or by a spherical (radially symmetric) kernel proportional to $K(||u||)$. (The resulting kernel is a density, i.e. integrates to 1.)

Examples

  kernel.function(0)                         ## default (biweight)
  kernel.function(0, kernel="epanechnikov")  ## epanechnikov
  kernel.function(0, kernel="gaussian")      ## equals dnorm(0)