CVarE (version 1.1)

estimate.bandwidth: Bandwidth estimation for CVE.

Description

If no bandwidth or function for calculating it is supplied, the CVE method defaults to using the following formula (version 1) $$% h = \frac{2 tr(\Sigma)}{p} (1.2 n^{\frac{-1}{4 + k}})^2$$ Alternative version 2 is used for dimension prediction which is given by $$% h = \frac{2 tr(\Sigma)}{p} \chi_k^{-1}(\frac{nObs - 1}{n - 1})$$ with \(n\) the sample size, \(p\) the dimension of \(X\) and \(\Sigma\) is \((n - 1) / n\) times the sample covariance matrix of \(X\).

Usage

estimate.bandwidth(X, k, nObs, version = 1L)

Arguments

X

the \(n\times p\) matrix of predictor values.

k

the SDR dimension.

nObs

number of points in a slice, only for version 2.

version

either 1 or 2.

Value

Estimated bandwidth h.

Examples

# NOT RUN {
# set dimensions for simulation model
p <- 5; k <- 1
# create B for simulation
B <- rep(1, p) / sqrt(p)
# samplsize
n <- 100
set.seed(21)
#creat predictor data x ~ N(0, I_p)
x <- matrix(rnorm(n * p), n, p)
# simulate response variable
#     y = f(B'x) + err
# with f(x1) = x1 and err ~ N(0, 0.25^2)
y <- x %*% B + 0.25 * rnorm(100)
# calculate cve with method 'simple' for k = 1
set.seed(21)
cve.obj.simple <- cve(y ~ x, k = k)
print(estimate.bandwidth(x, k = k))
# }