SIRasymp | 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.
SIRasymp(X, y, k, h = 10, ...)
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 |
... |
other arguments passed on to |
Under the null the first k
eigenvalues contained in D
are non-zero and the remaining p-k
are zero.
For a sample of size n, the test statistic T is then n times the sum of these last p-k eigenvalue and has under the null a chisquare distribution with (p-k)(h-k-1) degrees of freedom, therefore it is required that k < h-1.
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 degrees of freedom of the test. |
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
, SIRboot
X <- matrix(rnorm(1000), ncol = 5) eps <- rnorm(200, sd = 0.1) y <- 2 + 0.5 * X[, 1] + 2 * X[, 3] + eps SIRasymp(X, y, k = 0) SIRasymp(X, y, k = 1)
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