Sliced inverse moment regression using weighted chi-squared tests for dimension reduction

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...

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...

Localized Sliced Inverse Regression

We developed localized sliced inverse regression for supervised dimension reduction. It has the advantages of preventing degeneracy, increasing estimation accuracy, and automatic subclass discovery in classification problems. A semisupervised version is proposed for the use of unlabeled data. The utility is illustrated on simulated as well as real data sets.

Student Sliced Inverse Regression

Sliced Inverse Regression (SIR) has been extensively used to reduce the dimension of the predictor space before performing regression. SIR is originally a model free method but it has been shown to actually correspond to the maximum likelihood of an inverse regression model with Gaussian errors. This intrinsic Gaussianity of standard SIR may explain its high sensitivity to outliers as observed ...