Fast 'n' fair simultaneous confidence band (t-distr)

Usage

make_band_FFSCB_t(x, diag.cov.x, tau, df, conf.level = 0.95, n_int = 4)

Arguments

x: Functional parameter estimate.
diag.cov.x: Diagonal of Cov(x), in which x is the functional estimator (for instance, the covariance function of the empirical mean function).
tau: Pointwise standard deviation of the standardized and differentiated sample functions. Can be estimated by tau_fun().
df: Degrees of freedom
conf.level: confidence level (default: 0.95)
n_int: Number of equidistant intervals over which the multiple testing component of the type-I error rate (1-conf.level) is distributed uniformly.

References

Liebl, D. and Reimherr, M. (2022+). Fast and fair simultaneous confidence bands.

Examples

# Generate a sample
p          <- 200 
N          <- 80 
grid       <- make_grid(p, rangevals=c(0,1))
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))
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 
hat.tau    <- tau_fun(sample)

# Make and plot confidence bands
band <- make_band_FFSCB_t(x=hat.mu, diag.cov.x=diag(hat.cov.mu), tau=hat.tau,
                       df = N-1, conf.level  = 0.95)
matplot(y=band[,2:3], x=grid, lty=2)
lines(x=grid, y=band[,1], lty=1)