SIR: Classic SIR

In SIRthresholded: Sliced Inverse Regression with Thresholding

Classic SIR

Description

Apply a single-index SIR on (X,Y) with H slices. This function allows to obtain an estimate of a basis of the EDR (Effective Dimension Reduction) space via the eigenvector \hat{b} associated with the largest nonzero eigenvalue of the matrix of interest \widehat{\Sigma}_n^{-1}\widehat{\Gamma}_n. Thus, \hat{b} is an EDR direction.

Usage

SIR(Y, X, H = 10, graph = TRUE, choice = "")

Arguments

Y	A numeric vector representing the dependent variable (a response vector).
X	A matrix representing the quantitative explanatory variables (bind by column).
H	The chosen number of slices (default is 10).
graph	A boolean that must be set to true to display graphics (default is TRUE).
choice	the graph to plot: "eigvals" Plot the eigen values of the matrix of interest. "estim_ind" Plot the estimated index by the SIR model versus Y. "" Plot every graphs. (default)

Value

An object of class SIR, with attributes:

b	This is an estimated EDR direction, which is the principal eigenvector of the interest matrix.
M1	The interest matrix.
eig_val	The eigenvalues of the interest matrix.
n	Sample size.
p	The number of variables in X.
H	The chosen number of slices.
call	Unevaluated call to the function.
index_pred	The index Xb' estimated by SIR.
Y	The response vector.

Examples

# Generate Data
set.seed(10)
n <- 500
beta <- c(1,1,rep(0,8))
X <- mvtnorm::rmvnorm(n,sigma=diag(1,10))
eps <- rnorm(n)
Y <- (X%*%beta)**3+eps

# Apply SIR
SIR(Y, X, H = 10)

SIRthresholded documentation built on July 10, 2023, 2:03 a.m.