# BCIntervalSpearman: Bootstrap Confidence Interval on Spearman's Correlation... In roahd: Robust Analysis of High Dimensional Data

## Description

This function computes the bootstrap confidence interval of coverage probability 1 - α for the Spearman correlation coefficient between two univariate functional samples.

## Usage

 ```1 2 3 4 5 6 7 8``` ```BCIntervalSpearman( fD1, fD2, ordering = "MEI", bootstrap_iterations = 1000, alpha = 0.05, verbose = FALSE ) ```

## Arguments

 `fD1` is the first univariate functional sample in form of an `fData` object. `fD2` is the first univariate functional sample in form of an `fData` 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 interval (default is 1000). `alpha` controls the coverage probability (1-`alpha`). `verbose` whether to log information on the progression of bootstrap iterations.

## Details

The function takes two samples of compatible functional data (i.e., they must be defined over the same grid and have same number of observations) and computes a bootstrap confidence interval for their Spearman correlation coefficient.

## Value

The function returns a list of two elements, `lower` and `upper`, representing the lower and upper end of the bootstrap confidence interval.

`cor_spearman`, `cor_spearman_accuracy`, `fData`, `mfData`, `BCIntervalSpearmanMultivariate`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27``` ```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, centerline = sin( 2 * pi * grid ), Cov = Cov ) Data_2 <- generate_gauss_fdata( N = N, centerline = sin(2 * pi * grid), Cov = Cov ) # Using the simulated data as (independent) components of a bivariate functional dataset mfD <- mfData(grid, list(Data_1, Data_2)) BCIntervalSpearman(mfD\$fDList[[1]], mfD\$fDList[[2]], ordering = "MEI") BCIntervalSpearman(mfD\$fDList[[1]], mfD\$fDList[[2]], ordering = "MHI") # BC intervals contain zero since the functional samples are uncorrelated. ```