SIR_threshold: SIR threshold

In SIRthresholded: Sliced Inverse Regression with Thresholding

SIR threshold

Description

Apply a single-index SIR on (X,Y) with H slices, with a parameter \lambda which apply a soft/hard thresholding to the interest matrix \widehat{\Sigma}_n^{-1}\widehat{\Gamma}_n.

Usage

SIR_threshold(
  Y,
  X,
  H = 10,
  lambda = 0,
  thresholding = "hard",
  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).
lambda	The thresholding parameter (default is 0).
thresholding	The thresholding method to choose between hard and soft (default is hard).
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_threshold, with attributes:

b	This is an estimated EDR direction, which is the principal eigenvector of the interest matrix.
M1	The interest matrix thresholded.
eig_val	The eigenvalues of the interest matrix thresholded.
eig_vect	A matrix corresponding to the eigenvectors of the interest matrix.
Y	The response vector.
n	Sample size.
p	The number of variables in X.
H	The chosen number of slices.
nb.zeros	The number of 0 in the estimation of the vector beta.
index_pred	The index Xb' estimated by SIR.
list.relevant.variables	A list that contains the variables selected by the model.
cos_squared	The cosine squared between vanilla SIR and SIR thresholded.
lambda	The thresholding parameter used.
thresholding	The thresholding method used.
call	Unevaluated call to the function.
X_reduced	The X data restricted to the variables selected by the model. It can be used to estimate a new SIR model on the relevant variables to improve the estimation of b.

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 with hard thresholding
SIR_threshold(Y, X, H = 10, lambda = 0.2, thresholding = "hard")

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