Using sliced inverse mean difference for sufficient dimension reduction

Sliced Inverse Regression for Dimension Reduction

Sliced Regression for Dimension Reduction

By slicing the region of the response (Li, 1991, SIR) and applying local kernel regression (Xia et al., 2002, MAVE) to each slice, a new dimension reduction method is proposed. Compared with the traditional inverse regression methods, e.g. sliced inverse regression (Li, 1991), the new method is free of the linearity condition (Li, 1991) and enjoys much improved estimation accuracy. Compared wit...

Sliced Inverse Moment Regression Using Weighted Chi-Squared Tests for Dimension Reduction∗

We propose a new class of dimension reduction methods using the first two inverse moments, called Sliced Inverse Moment Regression (SIMR). We develop corresponding weighted chi-squared tests for the dimension of the regression. Basically, SIMR are linear combinations of Sliced Inverse Regression (SIR) and the method using a new candidate matrix which is designed to recover the entire inverse se...

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...

Sufficient Dimension Reduction Summaries

Observational studies assessing causal or non-causal relationships between an explanatory measure and an outcome can be complicated by hosts of confounding measures. Large numbers of confounders can lead to several biases in conventional regression based estimation. Inference is more easily conducted if we reduce the number of confounders to a more manageable number. We discuss use of sufficien...