FRESHD (version 1.0)

RH: The Rotated H-transform of a 3d Array by a Matrix

Description

This function is an implementation of the \(\rho\)-operator found in Currie et al 2006. It forms the basis of the GLAM arithmetic.

Usage

RH(M, A)

Arguments

M

a \(n \times p_1\) matrix.

A

a 3d array of size \(p_1 \times p_2 \times p_3\).

Value

A 3d array of size \(p_2 \times p_3 \times n\).

Details

For details see Currie et al 2006. Note that this particular implementation is not used in the routines underlying the optimization procedure.

References

Currie, I. D., M. Durban, and P. H. C. Eilers (2006). Generalized linear array models with applications to multidimensional smoothing. Journal of the Royal Statistical Society. Series B. 68, 259-280. url = http://dx.doi.org/10.1111/j.1467-9868.2006.00543.x.

Examples

# NOT RUN {
n1 <- 65; n2 <- 26; n3 <- 13; p1 <- 13; p2 <- 5; p3 <- 4

##marginal design matrices (Kronecker components)
X1 <- matrix(rnorm(n1 * p1), n1, p1)
X2 <- matrix(rnorm(n2 * p2), n2, p2)
X3 <- matrix(rnorm(n3 * p3), n3, p3)

Beta <- array(rnorm(p1 * p2 * p3, 0, 1), c(p1 , p2, p3))
max(abs(c(RH(X3, RH(X2, RH(X1, Beta)))) - kronecker(X3, kronecker(X2, X1)) %*% c(Beta)))

# }