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")
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 |
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 |
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.
Returns a matrix with the same dimensions of x where row i provides
the vector of smoothing parameters for sample point x_i.
Silverman, B. (1986). Density estimation for statistics and data analysis. Chapman and Hall, London.
h.norm
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))
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