This code implements the compositional smoothing splines grounded on the theory of Bayes spaces.
compositionalSpline(
t,
clrf,
knots,
w,
order,
der,
alpha,
spline.plot = FALSE,
basis.plot = FALSE
)Jvalue of the functional J
ZB_coefZB-spline basis coeffcients
CVscore of cross-validation
GCVscore of generalized cross-validation
class midpoints
clr transformed values at class midpoints, i.e., fcenLR(f(t))
sequence of knots
weights
order of the spline (i.e., degree + 1)
lth derivation
smoothing parameter
if TRUE, the resulting spline is plotted
if TRUE, the ZB-spline basis system is plotted
J. Machalova jitka.machalova@upol.cz, R. Talska talskarenata@seznam.cz
The compositional splines enable to construct a spline basis in the centred logratio (clr) space of density functions (ZB-spline basis) and consequently also in the original space of densities (CB-spline basis).The resulting compositional splines in the clr space as well as the ZB-spline basis satisfy the zero integral constraint. This enables to work with compositional splines consistently in the framework of the Bayes space methodology.
Augmented knot sequence is obtained from the original knots by adding #(order-1) multiple endpoints.
Machalova, J., Talska, R., Hron, K. Gaba, A. Compositional splines for representation of density functions. Comput Stat (2020). https://doi.org/10.1007/s00180-020-01042-7