fregion: fregion

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

Description

This package contains example codes for inferential tools suggested in http://arxiv.org/abs/1607.07771, titled 'Geometric Approach to Confidence Regions and Bands for Functional Parameters'. The top level functions below take functional estimate and the covariance of it to perform hypothesis testings, to construct confidence bands, and to construct/visuallize hyper-rectangular regions. The inputs can be either vector/matrix or fd/bifd object from fda package.

• fregion.test: Perform hypothesis testings based on confidence regions.

• fregion.band: Construct (simultaneous) confidence bands using hyper-ellipsoid confidence regions.

• fregion.rect: Construct a hyper-rectangular confidence region in Hilbert space. It can be visuzlized using plot.fregion.rect.

The example below is given in a mean function estimation context but works for other functional estimates as long as the estimators are Gaussian.

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.

# Compare different methods for Hypothesis testings.
(a1 <- fregion.test(hat.mu,mu0,hat.cov.m,N,type=c("ALL"),pc.cut=c(1,3,4,5,0.99,0.999)))

# Make and visualize/compare confidence bands
b <- fregion.band(hat.mu,hat.cov.m,N=N,type=c("Bs","BEc","BEPC.10","naive.t"),conf.level=c(0.95))
plot(b)

# 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.

# Compare different methods for Hypothesis testings.
(a1.fd <- fregion.test(hat.mu.fd, mu0.fd, hat.cov.fd, N, type=c("ALL"), pc.cut=c(1,3,4,5,0.99,0.999)))

# Make and visualize/compare confidence bands
b.fd <- fregion.band(hat.mu.fd,hat.cov.fd,N=N,type=c("Bs","BEc","BEPC.10","naive.t"),conf.level=c(0.95))
plot(b.fd)

# 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.