% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/plot.R
\name{plot.cve}
\alias{plot.cve}
\title{Elbow plot of the loss function.}
\usage{
\method{plot}{cve}(x, ...)
}
\arguments{
\item{x}{an object of class \code{"cve"}, usually, a result of a call to
\code{\link{cve}} or \code{\link{cve.call}}.}

\item{...}{Pass through parameters to [\code{\link{plot}}] and
[\code{\link{lines}}]}
}
\description{
Boxplots of the output \code{L} from \code{\link{cve}} over \code{k} from
\code{min.dim} to \code{max.dim}. For given \code{k}, \code{L} corresponds
to \eqn{L_n(V, X_i)} where \eqn{V} is the minimizer of \eqn{L_n(V)} where
\eqn{V} is an element of a Stiefel manifold (see
Fertl, L. and Bura, E. (2019)).
}
\examples{
# create B for simulation
B <- cbind(rep(1, 6), (-1)^seq(6)) / sqrt(6)

set.seed(21)
# creat predictor data x ~ N(0, I_p)
X <- matrix(rnorm(600), 100)

# simulate response variable
#    y = f(B'x) + err
# with f(x1, x2) = x1^2 + 2 x2 and err ~ N(0, 0.25^2)
Y <- (X \%*\% B[, 1])^2 + 2 * X \%*\% B[, 2] + rnorm(100, 0, .1)

# Create bandwidth estimation function
estimate.bandwidth <- function(X, k, nObs) {
    n <- nrow(X)
    p <- ncol(X)
    X_c <- scale(X, center = TRUE, scale = FALSE)
    2 * qchisq((nObs - 1) / (n - 1), k) * sum(X_c^2) / (n * p)
}
# calculate cve with method 'simple' for k = min.dim,...,max.dim
cve.obj.simple <- cve(Y ~ X, h = estimate.bandwidth, nObs = sqrt(nrow(X)))

# elbow plot
plot(cve.obj.simple)

}
\references{
Fertl, L. and Bura, E. (2019), Conditional Variance
Estimation for Sufficient Dimension Reduction. Working Paper.
}
\seealso{
see \code{\link{par}} for graphical parameters to pass through
     as well as \code{\link{plot}}, the standard plot utility.
}