% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/estimateBandwidth.R
\name{estimate.bandwidth}
\alias{estimate.bandwidth}
\title{Bandwidth estimation for CVE.}
\usage{
estimate.bandwidth(X, k, nObs)
}
\arguments{
\item{X}{data matrix with samples in its rows.}

\item{k}{Dimension of lower dimensional projection.}

\item{nObs}{number of points in a slice, see \eqn{nObs} in CVE paper.}
}
\value{
Estimated bandwidth \code{h}.
}
\description{
Estimates a bandwidth \code{h} according
\deqn{%
h = (2 * tr(\Sigma) / p) * (1.2 * n^{-1 / (4 + k)})^2}{%
h = (2 * tr(\Sigma) / p) * (1.2 * n^(\frac{-1}{4 + k}))^2}
with \eqn{n} the sample size, \eqn{p} its dimension
(\code{n <- nrow(X); p <- ncol(X)}) and the covariance-matrix \eqn{\Sigma}
which is \code{(n-1)/n} times the sample covariance estimate.
}
\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(cve.obj.simple$res$'1'$h)
print(estimate.bandwidth(x, k = k))
}