sync: man

CVE_C/man/cve.call.Rd

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+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/CVE.R
+\name{cve.call}
+\alias{cve.call}
+\title{Conditional Variance Estimator (CVE).}
+\usage{
+cve.call(X, Y, method = "simple", nObs = sqrt(nrow(X)), h = NULL,
+  min.dim = 1L, max.dim = 10L, k = NULL, momentum = 0, tau = 1,
+  tol = 0.001, slack = 0, gamma = 0.5, V.init = NULL,
+  max.iter = 50L, attempts = 10L, logger = NULL)
+}
+\arguments{
+\item{X}{data matrix with samples in its rows.}
+
+\item{Y}{Responses (1 dimensional).}
+
+\item{nObs}{parameter for choosing bandwidth \code{h} using
+\code{\link{estimate.bandwidth}} (ignored if \code{h} is supplied).}
+
+\item{h}{bandwidth or function to estimate bandwidth, defaults to internaly
+estimated bandwidth.}
+
+\item{min.dim}{lower bounds for \code{k}, (ignored if \code{k} is supplied).}
+
+\item{max.dim}{upper bounds for \code{k}, (ignored if \code{k} is supplied).}
+
+\item{k}{Dimension of lower dimensional projection, if \code{k} is given
+only the specified dimension \code{B} matrix is estimated.}
+
+\item{momentum}{number of [0, 1) giving the ration of momentum for eucledian
+gradient update with a momentum term.}
+
+\item{tau}{Initial step-size.}
+
+\item{tol}{Tolerance for break condition.}
+
+\item{slack}{Positive scaling to allow small increases of the loss while
+optimizing.}
+
+\item{gamma}{step-size reduction multiple.}
+
+\item{V.init}{Semi-orthogonal matrix of dimensions `(ncol(X), ncol(X) - k)` #'      as optimization starting value. (If supplied, \code{attempts} is
+set to 1 and \code{k} to match dimension)}
+
+\item{max.iter}{maximum number of optimization steps.}
+
+\item{attempts}{number of arbitrary different starting points.}
+
+\item{logger}{a logger function (only for advanced user, significantly slows
+down the computation).}
+}
+\value{
+an S3 object of class \code{cve} with components:
+\describe{
+   \item{X}{Original training data,}
+   \item{Y}{Responce of original training data,}
+   \item{method}{Name of used method,}
+   \item{call}{the matched call,}
+   \item{res}{list of components \code{V, L, B, loss, h} and \code{k} for
+              each \eqn{k=min.dim,...,max.dim} (dimension).}
+}
+}
+\description{
+Conditional Variance Estimation (CVE) is a novel sufficient dimension
+reduction (SDR) method for regressions satisfying \eqn{E(Y|X) = E(Y|B'X)},
+where \eqn{B'X} is a lower dimensional projection of the predictors. CVE,
+similarly to its main competitor, the mean average variance estimation
+(MAVE), is not based on inverse regression, and does not require the
+restrictive linearity and constant variance conditions of moment based SDR
+methods. CVE is data-driven and applies to additive error regressions with
+continuous predictors and link function. The effectiveness and accuracy of 
+CVE compared to MAVE and other SDR techniques is demonstrated in simulation
+studies. CVE is shown to outperform MAVE in some model set-ups, while it
+remains largely on par under most others.
+Let \eqn{Y} be real denotes a univariate response and \eqn{X} a real
+\eqn{p}-dimensional covariate vector. We assume that the dependence of
+\eqn{Y} and \eqn{X} is modelled by
+\deqn{Y = g(B'X) + \epsilon}
+where \eqn{X} is independent of \eqn{\epsilon} with positive definite
+variance-covariance matrix \eqn{Var(X) = \Sigma_X}. \eqn{\epsilon} is a mean
+zero random variable with finite \eqn{Var(\epsilon) = E(\epsilon^2)}, \eqn{g}
+is an unknown, continuous non-constant function,
+and \eqn{B = (b_1, ..., b_k)} is
+a real \eqn{p \times k}{p x k} of rank \eqn{k <= p}{k \leq p}. 
+Without loss of generality \eqn{B} is assumed to be orthonormal.
+}

CVE_C/man/predict.dim.Rd

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+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/predict_dim.R
+\name{predict.dim}
+\alias{predict.dim}
+\title{Predicts SDR dimension using \code{\link[mda]{mars}} via a Cross-Validation.}
+\usage{
+predict.dim(object, ...)
+}
+\arguments{
+\item{object}{instance of class \code{cve} (result of \code{cve},
+\code{cve.call}).}
+
+\item{...}{ignored.}
+}
+\value{
+list with
+\itemize{
+   \item MSE: Mean Square Error,
+   \item k: predicted dimensions.
+}
+}
+\description{
+Predicts SDR dimension using \code{\link[mda]{mars}} via a Cross-Validation.
+}