59 lines
1.9 KiB
R
59 lines
1.9 KiB
R
% Generated by roxygen2: do not edit by hand
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% Please edit documentation in R/predict_dim.R
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\name{predict_dim}
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\alias{predict_dim}
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\title{Estimate Dimension of the Sufficient Reduction.}
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\usage{
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predict_dim(object, ..., method = "CV")
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}
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\arguments{
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\item{object}{an object of class \code{"cve"}, usually, a result of a call to
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\code{\link{cve}} or \code{\link{cve.call}}.}
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\item{...}{ignored.}
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\item{method}{This parameter specifies which method is used in dimension
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estimation. It provides three options: \code{'CV'} (default),
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\code{'elbow'} and \code{'wilcoxon'}.}
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}
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\value{
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A \code{list} with
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\describe{
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\item{}{criterion for method and \code{k = min.dim, ..., max.dim}.}
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\item{k}{estimated dimension is the minimizer of the criterion.}
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}
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}
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\description{
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This function estimates the dimension, i.e. the rank of \eqn{B}. The default
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method \code{'CV'} performs leave-one-out (LOO) cross-validation using
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\code{mars} as follows for \code{k = min.dim, ..., max.dim} a
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cross-validation via \code{mars} is
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performed on the dataset \eqn{(Y_i, B_k' X_i)_{i = 1, ..., n}} where
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\eqn{B_k} is the \eqn{p \times k}{p x k} dimensional CVE estimate. The
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estimated SDR dimension is the \eqn{k} where the
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cross-validation mean squared error is minimal. The method \code{'elbow'}
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estimates the dimension via \eqn{k = argmin_k L_n(V_{p - k})} where
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\eqn{V_{p - k}} is the space that is orthogonal to the column space of the
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CVE estimate of \eqn{B_k}. Method \code{'wilcoxon'} finds the minimum using
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the Wilcoxon test.
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}
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\examples{
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# create B for simulation
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B <- rep(1, 5) / sqrt(5)
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set.seed(21)
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# creat predictor data x ~ N(0, I_p)
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x <- matrix(rnorm(500), 100)
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# simulate response variable
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# y = f(B'x) + err
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# with f(x1) = x1 and err ~ N(0, 0.25^2)
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y <- x \%*\% B + 0.25 * rnorm(100)
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# Calculate cve for unknown k between min.dim and max.dim.
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cve.obj.simple <- cve(y ~ x)
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predict_dim(cve.obj.simple)
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}
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