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Package: CVE |
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Package: CVarE |
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Type: Package |
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Title: Conditional Variance Estimator for Sufficient Dimension Reduction |
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Version: 0.3 |
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Date: 2021-03-04 |
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Author: Daniel Kapla <daniel@kapla.at>, Lukas Fertl <lukas.fertl@chello.at> |
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Version: 1.0 |
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Date: 2021-03-05 |
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Maintainer: Daniel Kapla <daniel@kapla.at> |
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Description: Implementation of the Conditional Variance Estimation (CVE) method. |
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Author: Daniel Kapla [aut, cph, cre], |
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Lukas Fertl [aut, cph], |
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Efstathia Bura [ctb] |
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Description: Implementation of the Conditional Variance Estimation (CVE) |
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Fertl and Bura (2021) <arXiv:2102.08782> and the Ensemble Conditional Variance |
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Estimation (ECVE) Fertl and Bura (2021) <arXiv:2102.13435> method. |
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|
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CVE and ECVE are sufficient dimension reduction (SDR) methods |
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in regressions with continuous response and predictors. CVE applies to general |
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additive error regression models while ECVE generalizes to non-additive error |
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regression models. They operate under the assumption that the predictors can |
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be replaced by a lower dimensional projection without loss of information. |
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It is a semiparametric forward regression model based exhaustive sufficient |
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dimension reduction estimation method that is shown to be consistent under mild |
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assumptions. |
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License: GPL-3 |
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Contact: <daniel@kapla.at> |
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URL: https://git.art-ist.cc/daniel/CVE |
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Encoding: UTF-8 |
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NeedsCompilation: yes |
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Imports: stats,mda |
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RoxygenNote: 7.0.2 |
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% 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{CVE-package} |
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\alias{CVE} |
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\alias{CVE-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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|
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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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|
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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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|
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\deqn{Y = g(B'X, \epsilon)} |
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|
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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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|
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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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\author{ |
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Daniel Kapla, Lukas Fertl, Bura Efstathia |
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} |
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