hprop2f function

Sample smoothing parameters in adaptive density estimation

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

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 $0 \leq \alpha \leq 1$, 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 $h_{i}$ is chosen for each sample point $x_i$, as follows:

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

Returns

Returns a matrix with the same dimensions of x where row $i$ provides the vector of smoothing parameters for sample point $x_i$.

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))