IHT: Iterative Hessian Transformation Regression

In abnormally-distributed/cvreg: Cross Validation and Robust Estimation Utilities

Description

Iterative Hessian transformation (IHT) regression was developed as a means of relaxing the constant conditional variance assumption required by SIR and SAVE. IHT only requires the linear conditional mean assumption, but like SAVE it is capable of recovering more directions in the central subspace than SIR. To be precise, IHT recovers directions in the central mean subspace (CMS)

The algorithm underlying IHT is fairly simple:

1. Calculate the covariance of X and Y, Cov_{xy} = cov(X, Y) and the covariance of the transposed crossproduct of X and Y, Cov_{xxy} = E[XX'Y].

2. Next, calculate a matrix where the first column is Cov_xy, and each following column is the product of Cov_xxy raised to the 1st to p-1th power in sequential order :

M = (Cov_{xy}, Cov_{xxy}Cov_{xy}, ... , Cov_{xxy}^{p-1}Cov_{xy})

3. Compute Λ = MM' and take the first r eigenvectors of Λ, where r is the desired rank of the set of sufficient predictors. The set of r eigenvectors are the sufficient predictors on the unit scale.

Usage

IHT(formula, data, rank = "all")

Arguments

formula	a model formula
data	a data frame
rank	the desired number of sufficient predictors to return. the default is "all". .

Value

an sdr object

abnormally-distributed/cvreg documentation built on May 3, 2020, 3:45 p.m.