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funbootband

funbootband computes simultaneous prediction and confidence bands for dense functional data observed on a common grid. Curves are represented by finite Fourier series before bootstrap calibration. The package supports independent curves and repeated curves nested within subjects.

For clustered data, version 0.3.0 uses an intact-subject bootstrap: subjects are sampled with replacement and all curves belonging to a selected subject are retained. Subjects receive equal weight, including when cluster sizes differ. The clustered prediction target is one Fourier-reconstructed future curve from an independent new subject.

Installation

Install the CRAN release with:

install.packages("funbootband")

Install the development version with:

# install.packages("pak")
pak::pak("koda86/funbootband-cran")

Independent curves

library(funbootband)

set.seed(1)
T <- 101L
n <- 30L
x <- seq(0, 1, length.out = T)
mu <- 0.7 * sin(2 * pi * x) - 0.2 * cos(4 * pi * x)

Y <- replicate(n, {
  mu + rnorm(1, sd = 0.35) +
    rnorm(1, sd = 0.30) * sin(2 * pi * x) +
    rnorm(1, sd = 0.20) * cos(2 * pi * x)
})

fit_pred <- band(Y, type = "prediction", alpha = 0.10,
                 iid = TRUE, B = 1000L, k.coef = 4L)
fit_conf <- band(Y, type = "confidence", alpha = 0.10,
                 iid = TRUE, B = 1000L, k.coef = 4L)

Repeated curves nested within subjects

set.seed(2)
K_subject <- 12L
m <- rep(c(2L, 3L, 4L), length.out = K_subject)
id <- rep(seq_len(K_subject), m)

subject_effect <- sapply(seq_len(K_subject), function(i) {
  rnorm(1, sd = 0.35) +
    rnorm(1, sd = 0.30) * sin(2 * pi * x) +
    rnorm(1, sd = 0.20) * cos(2 * pi * x)
})

Y_clustered <- sapply(seq_along(id), function(j) {
  mu + subject_effect[, id[j]] +
    rnorm(1, sd = 0.18) * sin(4 * pi * x) +
    rnorm(1, sd = 0.12) * cos(4 * pi * x)
})

fit_clustered <- band(
  Y_clustered,
  type = "prediction",
  alpha = 0.10,
  iid = FALSE,
  id = id,
  B = 1000L,
  k.coef = 4L
)

fit_clustered$meta[c(
  "target", "weighting", "bootstrap_unit", "n_clusters"
)]

The clustered band is marginal over the subject population. It is not a conditional band for an already observed subject and does not provide joint coverage for several future curves.

References

• Lenhoff et al. (1999) doi:10.1016/S0966-6362(98)00043-5
• Koska et al. (2023) doi:10.1016/j.jbiomech.2023.111506

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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