diff --git a/CVarE/inst/doc/Fertl_and_Bura-2021-CVE_for_SDR.pdf b/CVarE/inst/doc/Fertl_and_Bura-2021-CVE_for_SDR.pdf new file mode 100644 index 0000000..6afdd37 --- /dev/null +++ b/CVarE/inst/doc/Fertl_and_Bura-2021-CVE_for_SDR.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:46cd0cae7a91d4b8ecad48b3b83392b2710638d32c1ce40b2fbd65b89e726c14 +size 302181 diff --git a/CVarE/inst/doc/Fertl_and_Bura-2021-ECVE_for_SDR.pdf b/CVarE/inst/doc/Fertl_and_Bura-2021-ECVE_for_SDR.pdf new file mode 100644 index 0000000..97d810e --- /dev/null +++ b/CVarE/inst/doc/Fertl_and_Bura-2021-ECVE_for_SDR.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:286ccabb75733c53a56a7aaceba2ab507cdc1035f4dee71edb7ed455dcb2a233 +size 367134 diff --git a/CVarE/man/CVarE-package.Rd b/CVarE/man/CVarE-package.Rd new file mode 100644 index 0000000..c315ec4 --- /dev/null +++ b/CVarE/man/CVarE-package.Rd @@ -0,0 +1,62 @@ +% 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 +}