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CVarE/man/CVarE-package.Rd

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+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/CVE.R
+\docType{package}
+\name{CVarE-package}
+\alias{CVarE}
+\alias{CVarE-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 response. 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
+}
+\details{
+\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.
+
+Further, the extended Ensemble Conditional Variance Estimation (ECVE) is
+implemented which is a SDR method in regressions with continuous response and
+predictors. ECVE applies to general non-additive error regression models.
+
+\deqn{Y = g(B'X, \epsilon)}
+
+It operates under the assumption that the predictors can be replaced by a
+lower dimensional projection without loss of information.It is a
+semiparametric forward regression model based exhaustive sufficient dimension
+reduction estimation method that is shown to be consistent under mild
+assumptions.
+}
+\references{
+[1] Fertl, L. and Bura, E. (2021), Conditional Variance
+         Estimation for Sufficient Dimension Reduction.
+         arXiv:2102.08782
+
+   [2] Fertl, L. and Bura, E. (2021), Ensemble Conditional Variance
+         Estimation for Sufficient Dimension Reduction.
+         arXiv:2102.13435
+}
+\seealso{
+Useful links:
+\itemize{
+  \item \url{https://git.art-ist.cc/daniel/CVE}
+}
+
+}
+\author{
+Daniel Kapla, Lukas Fertl, Bura Efstathia
+}