63 lines
2.4 KiB
R
63 lines
2.4 KiB
R
% Generated by roxygen2: do not edit by hand
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% Please edit documentation in R/CVE.R
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\docType{package}
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\name{CVarE-package}
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\alias{CVarE}
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\alias{CVarE-package}
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\title{Conditional Variance Estimator (CVE) Package.}
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\description{
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Conditional Variance Estimation (CVE) is a novel sufficient dimension
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reduction (SDR) method for regressions satisfying \eqn{E(Y|X) = E(Y|B'X)},
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where \eqn{B'X} is a lower dimensional projection of the predictors and
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\eqn{Y} is a univariate response. CVE,
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similarly to its main competitor, the mean average variance estimation
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(MAVE), is not based on inverse regression, and does not require the
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restrictive linearity and constant variance conditions of moment based SDR
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methods. CVE is data-driven and applies to additive error regressions with
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continuous predictors and link function. Let \eqn{X} be a real
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\eqn{p}-dimensional covariate vector. We assume that the dependence of
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\eqn{Y} and \eqn{X} is modelled by
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}
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\details{
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\deqn{Y = g(B'X) + \epsilon}
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where \eqn{X} is independent of \eqn{\epsilon} with positive definite
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variance-covariance matrix \eqn{Var(X) = \Sigma_X}. \eqn{\epsilon} is a mean
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zero random variable with finite \eqn{Var(\epsilon) = E(\epsilon^2)}, \eqn{g}
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is an unknown, continuous non-constant function,
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and \eqn{B = (b_1, ..., b_k)} is
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a real \eqn{p \times k}{p x k} matrix of rank \eqn{k \leq p}{k <= p}.
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Without loss of generality \eqn{B} is assumed to be orthonormal.
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Further, the extended Ensemble Conditional Variance Estimation (ECVE) is
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implemented which is a SDR method in regressions with continuous response and
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predictors. ECVE applies to general non-additive error regression models.
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\deqn{Y = g(B'X, \epsilon)}
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It operates under the assumption that the predictors can be replaced by a
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lower dimensional projection without loss of information.It is a
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semiparametric forward regression model based exhaustive sufficient dimension
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reduction estimation method that is shown to be consistent under mild
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assumptions.
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}
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\references{
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[1] Fertl, L. and Bura, E. (2021) "Conditional Variance
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Estimation for Sufficient Dimension Reduction"
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<arXiv:2102.08782>
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[2] Fertl, L. and Bura, E. (2021) "Ensemble Conditional Variance
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Estimation for Sufficient Dimension Reduction"
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<arXiv:2102.13435>
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}
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\seealso{
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Useful links:
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\itemize{
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\item \url{https://git.art-ist.cc/daniel/CVE}
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}
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}
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\author{
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Daniel Kapla, Lukas Fertl, Bura Efstathia
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}
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