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SIR threshold

SIR_threshold.Rd

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")
#> 
#> Call:
#> SIR_threshold(Y = Y, X = X, H = 10, lambda = 0.2, thresholding = "hard")
#> 
#> Results of EDR directions estimation:
#> 
#>     Estimated direction
#> X1                0.712
#> X2                0.702
#> X3                0.000
#> X4                0.000
#> X5                0.000
#> X6                0.000
#> X7                0.000
#> X8                0.000
#> X9                0.000
#> X10               0.000
#>