hprop2f {pdfCluster}R Documentation

Sample smoothing parameters in adaptive density estimation

Description

This function computes the sample smoothing parameters to be used in adaptive kernel density estimation, according to Silverman (1986).

Usage

hprop2f(x, h = h.norm(x), alpha = 1/2, kernel = "gaussian")

Arguments

x

Vector or matrix of data.

h

Vector of smoothing parameters to be used to get a pilot estimate of the density function. It has length equal to NCOL(x).

alpha

Sensitivity parameter satysfying 0α10 \leq \alpha \leq 1, giving the power to which raise the pilot density. Default value is 1/2. See details.

kernel

Kernel to be used to compute the pilot density estimate. It should be one of "gaussian" or "t7". See kepdf for further details.

Details

A vector of smoothing parameters hih_{i} is chosen for each sample point xix_i, as follows:

hi=h(f^h(xi)g)αh_i = h \left(\frac{\hat{f}_h(x_i)}{g}\right)^{- \alpha }

where f^h\hat{f}_h is a pilot kernel density estimate of the density function ff, with vector of bandwidths h, and gg is the geometric mean of f^h(xi)\hat{f}_h(x_i), i=1,...,ni=1, ..., n. See Section 5.3.1 of the reference below.

Value

Returns a matrix with the same dimensions of x where row ii provides the vector of smoothing parameters for sample point xix_i.

References

Silverman, B. (1986). Density estimation for statistics and data analysis. Chapman and Hall, London.

See Also

h.norm

Examples

set.seed(123)
x <- rnorm(10)

sm.par <- hprop2f(x)
pdf <- kepdf(x, bwtype= "adaptive")

pdf@par$hx
sm.par

plot(pdf,eval.points=seq(-4,4,by=.2))

[Package pdfCluster version 1.0-4 Index]