This function computes the bootstrap estimates of standard error and bias of the Spearman's correlation coefficient for a multivariate functional dataset.
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a multivariate functional dataset whose Spearman's correlation
coefficient must be computed, in form of multivariate
the ordering relation to use on functional observations,
the number of bootstrap iterations to be used for estimation of bias and standard error.
a logical flag specifying whether to log information on the estimation progress.
Given a multivariate functional dataset X_1^(i), …, X_n^(i), i=0, …, L defined over the grid I = t_0, …, t_P, having components i=1, …, L, and a chosen ordering strategy (MEI or MHI), the function computes the matrix of Spearman's correlation indices of the dataset components, as well as their bias and standard deviation estimates through a specified number of bootstrap iterations (bias and standard error are updated with on-line formulas).
a list of three elements:
mean, the mean of the matrix of
bias, a matrix containing the estimated
bias (mean - point estimate of correlation coefficients);
matrix containing the estimated standard deviation of the coefficients'
matrix. In case the multivariate functional dataset has only two
components, the return type is scalar and not matrix.
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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(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)) # Computes bootstrap estimate of Spearman correlation cor_spearman_accuracy(mfD, ordering = "MEI") cor_spearman_accuracy(mfD, ordering = "MHI")
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