CVE-package {CVE}R Documentation

Conditional Variance Estimator (CVE) Package.

Description

Conditional Variance Estimation (CVE) is a novel sufficient dimension reduction (SDR) method for regressions satisfying E(Y|X) = E(Y|B'X), where B'X is a lower dimensional projection of the predictors and 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 X be a real p-dimensional covariate vector. We assume that the dependence of Y and X is modelled by

Y = g(B'X) + ε

where X is independent of ε with positive definite variance-covariance matrix Var(X) = Σ_X. ε is a mean zero random variable with finite Var(ε) = E(ε^2), g is an unknown, continuous non-constant function, and B = (b_1, ..., b_k) is a real p x k matrix of rank k <= p. Without loss of generality B is assumed to be orthonormal.

Author(s)

Daniel Kapla, Lukas Fertl, Bura Efstathia

References

Fertl, L. and Bura, E. (2019), Conditional Variance Estimation for Sufficient Dimension Reduction. Working Paper.


[Package CVE version 0.2 Index]