% 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, version = 1L)
}
\arguments{
\item{X}{the \eqn{n\times p}{n x p} matrix of predictor values.}

\item{k}{the SDR dimension.}

\item{nObs}{number of points in a slice, only for version 2.}

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