fregion.rect: Builds a Rectangular Confidence Region

In hpchoi/fregion: Confidence Regions and Bands for Functional Data

Description

Builds a Rectangular Confidence Region

Usage

fregion.rect(x, cov, N = 1, type = "Rz", conf.level = 0.95,
  pc.cut = 0.999, df = NULL)

Arguments

x	Functional parameter estimate. It can be either a vector or fd object from fda.
cov	N * Cov(X), in which X is the functional estimator. It can be either matrix or bifd object from fda. The eigen decomposition of Cov(X) can be used instead.
N	It should be '1' if 'cov' is the covariance operator for X itself, which is the default value.
type	This specifies which rectangular region to be constructed. It should be either one of "Rz", "Rz1", "Rzs", or "Rz1s".
conf.level	Confidence level of the region.
pc.cut	A numeric value. For integer values, fPC up to those values will be used. If it's a value from 0 to 1, this specifies the proportion of (estimated) variance that should be explained by the fPCs. If it is 0, all the available fPCs will be used as long as the size of eigenvalues are greater than .Machine$double.eps.
df	Degree of freedom to use in small sample versions.

Value

fregion.rect Use plot.fregion.rect to visualize.

Examples

# 1. Vector/matrix version

# Generate a sample
p = 200 ; N = 80 ; rangeval = c(0,1)
grid = make.grid(p, rangevals=rangeval)
mu0 = meanf.poly(grid,c(0,1)) ; names(mu0) = grid
mu = meanf.poly(grid,c(0,1.1)) ; names(mu) = grid
cov.m = make.cov.m(cov.f = covf.st.matern, grid=grid, cov.f.params=c(2/2,1,1))
x = make.sample(mu,cov.m,N)

# Find the estimate and covariance
hat.mu = rowMeans(x)
hat.cov.m = crossprod(t(x - hat.mu)) / (N-1)
e.hat.cov.m = eigen(hat.cov.m)   # <- This is optional and can be provide into the functions instead of hat.cov.m below.

# Make rectangular region and visulize
c <- fregion.rect(hat.mu-mu0,hat.cov.m,N=N)
plot(c)


# 2. fd/bifd version

# create basis, convert vector/matrix into fd/bifd objects.
require(fda)
nbasis <- round(p*0.9)
fd.basis <- create.bspline.basis(rangeval,nbasis)
mu0.fd <- Data2fd(names(mu0),mu0,fd.basis)
mu.fd <- Data2fd(names(mu),mu,fd.basis)
x.fd <- Data2fd(rownames(x),x,fd.basis)
hat.mu.fd <- mean.fd(x.fd)
hat.cov.fd <- var.fd(x.fd)
e.hat.cov.fd <- eigen.fd(hat.cov.fd)   # <- This is optional and can be provide into the functions instead of hat.cov.fd below.

# Make rectangular region and visulize
c.fd <- fregion.rect(hat.mu.fd-mu0.fd,hat.cov.fd,N=N)
plot(c.fd)

hpchoi/fregion documentation built on May 17, 2019, 4:53 p.m.