cv.BPST: Cross-validation using Bivariate Penalized Spline over...

In FIRST-Data-Lab/BPST: Bivariate Spline over Triangulation

Cross-validation using Bivariate Penalized Spline over Triangulation

Description

This function implements k-fold cross-validation via bivariate penlized spline over triangulation, and returns the mean squared prediction error.

Usage

cv.BPST(
  Y,
  Z,
  V,
  Tr,
  d = 5,
  r = 1,
  lambda = 10^seq(-6, 6, by = 0.5),
  nfold = 10,
  Hmtx = TRUE,
  Kmtx = TRUE,
  QR = TRUE,
  TA = TRUE
)

Arguments

Y	The response variable observed over the domain.
Z	The cooridinates of dimension n by two. Each row is the coordinates of a point.
V	The N by two matrix of vertices of a triangulation, where N is the number of vertices. Each row is the coordinates for a vertex.
Tr	The triangulation matrix of dimention nT by three, where nT is the number of triangles in the triangulation. Each row is the indices of vertices in V.
d	The degree of piecewise polynomials – default is 5, and usually d is greater than one. -1 represents piecewise constant.
r	The smoothness parameter – default is 1, and 0 \le r < d.
lambda	The tuning parameter – default is 10^(-6,-5.5,-5,\ldots,5,5.5,6).
Hmtx	The indicator of whether the smoothness matrix H need to be generated – default is TRUE.
Kmtx	The indicator of whether the energy matrix K need to be generated – default is TRUE.
QR	The indicator of whether a QR decomposition need to be performed on the smoothness matrix – default is TRUE.
TA	The indicator of whether the area of the triangles need to be calculated – default is TRUE.
nfolds	The number of folds – default is 10. Although nfold can be as large as the sample size (leave-one-out CV), it is not recommended for large datasets. Smallest value allowable for nfolds is 3.

Details

This R program is modified based on the Matlab program written by Ming-Jun Lai from the University of Georgia and Li Wang from the Iowa State University.

Value

lamc	The tuning parameter selected by k-fold cross validation (CV).
mspe	The mean squared prediction error calculated by k-fold cross validation (CV).

Examples

# Triangulation
# Option 1;
data(V1); data(Tr1); d=5; r=1; V=V1; Tr=Tr1;
# Option 2
# data(V2); data(Tr2); d=5; r=1; V=V2; Tr=Tr2;
d=-1; r=1;
# Grid Points
n1.grid=101; n2.grid=101; n.grid=n1.grid*n2.grid;
u.grid=seq(0,1,length.out=n1.grid)
v.grid=seq(0,1,length.out=n2.grid)
uu.grid=rep(u.grid,each=n2.grid)
vv.grid=rep(v.grid,times=n1.grid)
Z.grid=as.matrix(cbind(uu.grid,vv.grid))
func=1; sigma=0.1;
gridpoints=data.BPST(Z.grid,V,Tr,func,sigma,2019)
Y.grid=gridpoints$Y; mu.grid=gridpoints$mu;
ind=gridpoints$ind; ind.grid=(1:n.grid)[ind==1];
# Simulation parameters
n=2000;
ind.sam=sort(sample(ind.grid,n))
Y=as.matrix(gridpoints$Y[ind.sam]); Z=as.matrix(gridpoints$Z[ind.sam,]);
cv.BPST(Y,Z,V,Tr,d,r,lambda=10^seq(-6,6,by=0.5),nfold=10)

FIRST-Data-Lab/BPST documentation built on Sept. 18, 2023, 7:31 a.m.