ffscb

This package contains example codes for inferential tools suggested in Liebl and Reimherr (2019), titled 'Fast and Fair Simultaneous Confidence Bands for Functional Parameters'. The top level functions allow to construct simultaneous confidence bands and pvalue functions. The inputs can be either vector/matrix or fd/bifd object from fda package.

References

Liebl, D. and Reimherr, M. (2019). Fast and fair simultaneous confidence bands for functional parameters.

Examples

# Generate a sample
p          <- 200 
N          <- 80 
grid       <- make_grid(p, rangevals=c(0,1))
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))
sample     <- make_sample(mu,cov.m,N)

# Compute the estimate and its covariance
hat.mu     <- rowMeans(sample)
hat.cov    <- crossprod(t(sample - hat.mu)) / N
hat.cov.mu <- hat.cov / N

# Compute the tau-parameter (for the KR- and FFSCB-bands)
hat.tau    <- tau_fun(sample)

# Make and plot confidence bands
b <- confidence_band(x=hat.mu, cov.x=hat.cov.mu, tau=hat.tau, df=N-1,
                     type=c("FFSCB.t", "Bs","BEc","naive.t"),
                     conf.level  = 0.95)
plot(b)
lines(x=grid, y=mu0, lty=2)