CVE/CVE/man/CVE-package.Rd

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\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 and
\eqn{Y} is a univariate responce. 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. Let \eqn{X} be 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} matrix of rank \eqn{k \leq p}{k <= p}. 
Without loss of generality \eqn{B} is assumed to be orthonormal.
}
\references{
Fertl, L. and Bura, E. (2019), Conditional Variance
Estimation for Sufficient Dimension Reduction. Working Paper.
}
\author{
Daniel Kapla, Lukas Fertl, Bura Efstathia
}