CVarE-package {CVarE} 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 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 X be a real p-dimensional covariate vector. We assume that the dependence of Y and X is modelled by

### Details

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.

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.

Y = g(B'X, ε)

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.

### Author(s)

Daniel Kapla, Lukas Fertl, Bura Efstathia

### 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>