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

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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 ≤q α ≤q 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:

h_i = h ≤ft(\frac{\hat{f}_h(x_i)}{g}\right)^{- α }

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.

Value

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

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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))