Bootstrap SIR

Apply a single-index \(SIR\) on \(B\) bootstraped samples of \((X,Y)\) with \(H\) slices.

Usage

SIR_bootstrap(Y, X, H = 10, B = 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).

B

The number of bootstrapped samples to draw (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_bootstrap, with attributes:

b

This is an estimated EDR direction, which is the principal eigenvector of the interest matrix.

mat_b

A matrix of size p*B that contains an estimation of beta in the columns for each bootstrapped sample.

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 b'X 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 bootstrap SIR
SIR_bootstrap(Y, X, H = 10, B = 10)
#> 
#> Call:
#> SIR_bootstrap(Y = Y, X = X, H = 10, B = 10)
#> 
#> Results of EDR directions estimation:
#> 
#>     Estimated direction
#> X1              0.71000
#> X2              0.70000
#> X3              0.02060
#> X4             -0.03230
#> X5             -0.00665
#> X6             -0.06550
#> X7             -0.02100
#> X8             -0.00582
#> X9              0.00288
#> X10             0.00845
#>