Permutation test for dimensionality

Approximates marginal dimension test significance levels by sampling from the permutation distribution.

Usage

msir.permutation.test(object, npermute = 99, numdir = object$numdir, verbose = TRUE)

Arguments

object: a 'msir' object.
npermute: number of permutations to compute.
numdir: maximum value of the dimension to test.
verbose: if TRUE a textual progress bar is shown during computation.

Details

The function approximates significance levels of the marginal dimension tests based on a permutation test.

Value

The function returns a list with components:

summary: a table containing the hypotheses, the test statistics, the permutation p-values.
npermute: the number of permutations used.

Furthermore, it also assigns the above information to the corresponding 'msir' object.

References

Scrucca, L. (2011) Model-based SIR for dimension reduction. Computational Statistics & Data Analysis, 55(11), 3010-3026.

Author

Luca Scrucca luca.scrucca@unipg.it

Examples

if (FALSE) { # \dontrun{
# 1-dimensional simple regression
n <- 200
p <- 5
b <- as.matrix(c(1,-1,rep(0,p-2)))
x <- matrix(rnorm(n*p), nrow = n, ncol = p)
y <- exp(0.5 * x%*%b) + 0.1*rnorm(n)
MSIR <- msir(x, y)
msir.permutation.test(MSIR)
summary(MSIR)
} # }