Basis expansion of the coefficient function (MVSML eq. 14.2)

beta(t) = sum_{l=1}^{L1} beta_l phi_l(t), the device that makes eq. (14.1) estimable: an infinite-dimensional unknown function is replaced by L1 scalars, after which (14.1) collapses to the ordinary linear model (14.3).

Usage

Msm262(t, beta_coef, kind = "fourier", period = NULL)

Arguments

t: Numeric grid of evaluation points.
beta_coef: Numeric basis coefficients beta_1..beta_L1.
kind: Basis family, "fourier" or "poly".
period: Optional Fourier period; the grid span by default.

Value

List with beta_t, t, n_basis.

Details

This is the named R arm of module msm262. The expansion itself is implemented once, in Basexp of gp_mvsml_ch9_14.R; this entry point only exports it under the module's own name.

References

Montesinos Lopez, Montesinos Lopez and Crossa (2022), Multivariate Statistical Machine Learning Methods for Genomic Prediction, Springer, eq. (14.2) p.579, doi:10.1007/978-3-030-89010-0 .

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Msm262(V, V)
#> $beta_t
#> [1]  0.0466898  1.9700053 -4.3525184  4.0663101 -1.5859624 -9.1445245 16.0000000
#> [8]  0.0466898
#> 
#> $t
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $n_basis
#> [1] 8
#>