On expectile-assisted inverse regression estimation for sufficient dimension reduction

Sufficient Dimension Reduction via Inverse Regression: A Minimum Discrepancy Approach

A family of dimension-reduction methods, the inverse regression (IR) family, is developed by minimizing a quadratic objective function. An optimal member of this family, the inverse regression estimator (IRE), is proposed, along with inference methods and a computational algorithm. The IRE has at least three desirable properties: (1) Its estimated basis of the central dimension reduction subspa...

Sliced Inverse Regression for Dimension Reduction

Sufficient dimension reduction and prediction in regression.

Dimension reduction for regression is a prominent issue today because technological advances now allow scientists to routinely formulate regressions in which the number of predictors is considerably larger than in the past. While several methods have been proposed to deal with such regressions, principal components (PCs) still seem to be the most widely used across the applied sciences. We give...

Efficient Estimation in Sufficient Dimension Reduction.

We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model. This conversion allows us to derive an efficient estimator which reaches the optimal semiparametric efficiency bound...

Abundant Inverse Regression Using Sufficient Reduction and Its Applications

Statistical models such as linear regression drive numerous applications in computer vision and machine learning. The landscape of practical deployments of these formulations is dominated by forward regression models that estimate the parameters of a function mapping a set of p covariates, x , to a response variable, y. The less known alternative, Inverse Regression, offers various benefits tha...