CVE/CVE_C/man/CVE-package.Rd

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% Please edit documentation in R/CVE.R
\docType{package}
\name{CVE-package}
\alias{CVE}
\alias{CVE-package}
\title{Conditional Variance Estimator (CVE) Package.}
\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.
}
\details{
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.
}
\references{
Fertl Lukas, Bura Efstathia. Conditional Variance Estimation for
Sufficient Dimension Reduction, 2019
}
\author{
Daniel Kapla, Lukas Fertl, Bura Efstathia
}