% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/predict_dim.R
\name{predict_dim}
\alias{predict_dim}
\title{Estimate Dimension of Reduction Space.}
\usage{
predict_dim(object, ..., method = "CV")
}
\arguments{
\item{object}{instance of class \code{cve} (result of \code{\link{cve}},
\code{\link{cve.call}}).}

\item{...}{ignored.}

\item{method}{This parameter specify which method will be used in dimension
estimation. It provides three methods \code{'CV'} (default), \code{'elbow'},
and \code{'wilcoxon'} to estimate the dimension of the SDR.}
}
\value{
list with
\describe{
   \item{}{cretirion of method for \code{k = min.dim, ..., max.dim}.}
   \item{k}{estimated dimension as argmin over \eqn{k} of criterion.}
}
}
\description{
This function estimates the dimension of the mean dimension reduction space,
i.e. number of columns of \eqn{B} matrix. The default method \code{'CV'}
performs cross-validation using \code{mars}. Given
\code{k = min.dim, ..., max.dim} a cross-validation via \code{mars} is
performed on the dataset \eqn{(Y i, B_k' X_i)_{i = 1, ..., n}} where
\eqn{B_k} is the \eqn{p \times k}{p x k} dimensional CVE estimate given
\eqn{k}. The estimated SDR dimension is the \eqn{k} where the
cross-validation mean squared error is the lowest. The method \code{'elbow'}
estimates the dimension via \eqn{k = argmin_k L_n(V_{p − k})} where
\eqn{V_{p − k}} is the CVE estimate of the orthogonal columnspace of
\eqn{B_k}. Method \code{'wilcoxon'} is similar to \code{'elbow'} but finds
the minimum using the wilcoxon-test.
}
\examples{
# create B for simulation
B <- rep(1, 5) / sqrt(5)

set.seed(21)
# creat predictor data x ~ N(0, I_p)
x <- matrix(rnorm(500), 100)

# 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 for unknown k between min.dim and max.dim.
cve.obj.simple <- cve(y ~ x) 

predict_dim(cve.obj.simple)

}