covSIR {ICtest}

Supervised Scatter Matrix as Used in Sliced Inverse Regression

Description

Sliced Inverse Regression (SIR) can be seen as special case of Supervised ICS (SICS) and this function gives the supervised scatter matrix for SIR

Usage

covSIR(X, y, h = 10, ...)

Arguments

X

a numeric data matrix.

y

a numeric response vector.

h

the number of slices.

...

arguments passed on to quantile.

Details

This supervised scatter matrix is usually used as the second scatter matrix in SICS to obtain a SIR type supervised linear dimension reduction. For that purpose covSIR first divides the response y into h slices using the corresponding quantiles as cut points. Then for each slice the mean vector of X is computed and the resulting supervised scatter matrix consist of the covariance matrix of these mean vectors.

The function might have problems if the sample size is too small.

Value

a supervised scatter matrix

Author(s)

Klaus Nordhausen

References

Liski, E., Nordhausen, K. and Oja, H. (2014), Supervised invariant coordinate selection, Statistics: A Journal of Theoretical and Applied Statistics, 48, 711–731. <doi:10.1080/02331888.2013.800067>.

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>.

See Also

ics

Examples

X <- matrix(rnorm(1000), ncol = 5)
eps <- rnorm(200, sd = 0.1)
y <- 2 + 0.5 * X[, 1] + 2 * X[, 3] + eps

covSIR(X, y)