Bootstrap Confidence Bands for Elastic Karcher Mean

Construct pointwise bootstrap confidence bands for the elastic Karcher mean by resampling curves and recomputing the mean for each bootstrap replicate.

Usage

shape.confidence.interval(
  fdataobj,
  n.bootstrap = 200,
  confidence.level = 0.95,
  lambda = 0,
  max.iter = 15,
  tol = 1e-04,
  seed = 42
)

Arguments

fdataobj

An object of class 'fdata'.

n.bootstrap

Number of bootstrap replicates (default 200).

confidence.level

Confidence level for the bands (default 0.95).

lambda

Regularisation parameter controlling warping smoothness (default 0).

max.iter

Maximum number of Karcher mean iterations per replicate (default 15).

tol

Convergence tolerance for each Karcher mean computation (default 1e-4).

seed

Random seed for reproducibility (default 42).

Value

An object of class 'shape.ci' with components:

mean

fdata of the Karcher mean curve

lower

numeric vector of lower confidence band values

upper

numeric vector of upper confidence band values

confidence.level

the confidence level used

n.bootstrap

the number of bootstrap replicates used

argvals

the evaluation grid

References

Tucker, J.D., Wu, W., and Srivastava, A. (2013). Generative models for functional data using phase and amplitude separation. Computational Statistics & Data Analysis, 61:50–66.

See also

karcher.mean

Examples

# \donttest{
set.seed(1)
t <- seq(0, 1, length.out = 50)
X <- matrix(0, 20, 50)
for (i in 1:20) X[i, ] <- sin(2 * pi * t + runif(1, -0.2, 0.2))
fd <- fdata(X, argvals = t)
ci <- shape.confidence.interval(fd, n.bootstrap = 50)
# }