SIRboot | R Documentation |
Using the two scatter matrices approach (SICS) for sliced inversion regression (SIR) the function tests
if the last p-k
components have zero eigenvalues, where p
is the number of explaining variables. Hence the assumption is that the first k
components are relevant for modelling the response y
and the remaining components are not. The function performs bootstrapping to obtain a p-value.
SIRboot(X, y, k, h = 10, n.boot = 200, ...)
X |
a numeric data matrix of explaining variables. |
y |
a numeric vector specifying the response. |
k |
the number of relevant components under the null hypothesis. |
h |
the number of slices used in SIR. Passed on to function |
n.boot |
number of bootstrapping samples. |
... |
other arguments passed on to |
Under the null hypthesis the last p-k eigenvalue as given in D are zero. The test statistic is then the sum of these eigenvalues.
Denote W as the transformation matrix to the supervised invariant coordinates (SIC) s_i, i=1,…,n, i.e.
s_i = W (X_i-MU),
where MU
is the location.
Let S_1 be the submatrix of the SICs which are relevant and S_2 the submatrix of the SICs which are irrelevant for the response y under the null.
The boostrapping has then the following steps:
Take a boostrap sample (y^*, S_1^*) of size n from (y, S_1).
Take a boostrap sample S_2^* of size n from S_2.
Combine S^*=(S_1^*, S_2^*) and create X^*= S^* W.
Compute the test statistic based on X^*.
Repeat the previous steps n.boot
times.
A list of class ictest inheriting from class htest containing:
statistic |
the value of the test statistic. |
p.value |
the p-value of the test. |
parameter |
the number of boostrapping samples used to compute the p-value. |
method |
character string which test was performed. |
data.name |
character string giving the name of the data. |
alternative |
character string specifying the alternative hypothesis. |
k |
the number of non-zero eigenvalues used in the testing problem. |
W |
the transformation matrix to the underlying components. |
S |
data matrix with the centered underlying components. |
D |
the underlying eigenvalues. |
MU |
the location of the data which was substracted before calculating the components. |
Klaus Nordhausen
Nordhausen, K., Oja, H. and Tyler, D.E. (2022), Asymptotic and Bootstrap Tests for Subspace Dimension, Journal of Multivariate Analysis, 188, 104830. <doi:10.1016/j.jmva.2021.104830>.
covSIR
, SIRasymp
X <- matrix(rnorm(1000), ncol = 5) eps <- rnorm(200, sd = 0.1) y <- 2 + 0.5 * X[, 1] + 2 * X[, 3] + eps SIRboot(X, y, k = 0) SIRboot(X, y, k = 1)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.