Bootstrap Confidence Interval on Spearman's Correlation Coefficient of a Multivariate Functional Dataset

Source: R/bootstrap_spearman_inference.R

This function computes the bootstrap confidence intervals of coverage probability \(1 - \alpha\) for the Spearman correlation coefficients within a multivariate functional dataset.

BCIntervalSpearmanMultivariate(
  mfD,
  ordering = "MEI",
  bootstrap_iterations = 1000,
  alpha = 0.05,
  verbose = FALSE
)

Arguments

mfD

is the multivariate functional sample in form of mfData object.

ordering

is either MEI (default) or MHI, and indicates the ordering relation to be used during in the Spearman's coefficient computation.

bootstrap_iterations

is the number of bootstrap iterations to use in order to estimate the confidence intervals (default is 1000).

alpha

controls the coverage probability (1-alpha).

verbose

whether to log information on the progression of bootstrap iterations.

Value

The function returns a list of two elements, lower and upper, representing the matrices of lower and upper ends of the bootstrap confidence intervals for each pair of components. The elements on the main diagonal are set to 1.

Details

The function takes a multivariate functional dataset and computes a matrix of bootstrap confidence intervals for its Spearman correlation coefficients.

Examples

set.seed(1)

N <- 200
P <- 100
grid <- seq(0, 1, length.out = P)

# Creating an exponential covariance function to simulate Gaussian data
Cov <- exp_cov_function(grid, alpha = 0.3, beta = 0.4)

# Simulating (independent) Gaussian functional data with given center and covariance function
Data_1 <- generate_gauss_fdata(
  N = N,
  centerline = sin(2 * pi * grid),
  Cov = Cov
)
Data_2 <- generate_gauss_fdata(
  N = N,
  centerline = sin(4 * pi * grid),
  Cov = Cov
)
Data_3 <- generate_gauss_fdata(
  N = N,
  centerline = sin(6 * pi * grid),
  Cov = Cov
)

# Using the simulated data as (independent) components of a multivariate functional dataset
mfD <- mfData(grid, list(Data_1, Data_2, Data_3))

# \donttest{
BCIntervalSpearmanMultivariate(mfD, ordering = "MEI")
#> $lower
#>             [,1]        [,2]       [,3]
#> [1,]  1.00000000 -0.09398461 -0.2570364
#> [2,] -0.09398461  1.00000000 -0.3056464
#> [3,] -0.25703636 -0.30564645  1.0000000
#> 
#> $upper
#>            [,1]        [,2]        [,3]
#> [1,] 1.00000000  0.15779563  0.02262386
#> [2,] 0.15779563  1.00000000 -0.02878122
#> [3,] 0.02262386 -0.02878122  1.00000000
#> 
# }

# BC intervals contain zero since the functional samples are uncorrelated.