estimate.bandwidth: Bandwidth estimation for CVE.

In CVarE: Conditional Variance Estimator for Sufficient Dimension Reduction

Description

If no bandwidth or function for calculating it is supplied, the CVE method defaults to using the following formula (version 1)

h = (2 * tr(Σ) / p) * (1.2 * n^(-1 / (4 + k)))^2

Alternative version 2 is used for dimension prediction which is given by

h = (2 * tr(Σ) / p) * χ_k^-1((nObs - 1) / (n - 1))

with n the sample size, p the dimension of X and Σ is (n - 1) / n times the sample covariance matrix of X.

Usage

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

Arguments

X	the n x 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

# 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))

CVarE documentation built on March 11, 2021, 5:06 p.m.