SIR | R Documentation |
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.
SIR(Y, X, H = 10, graph = TRUE, choice = "")
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:
|
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. |
# 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)
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