KTMatrixEst {ElliptCopulas}

Fast estimation of Kendall's tau matrix

Description

Estimate Kendall's tau matrix using averaging estimators. Under the structural assumption that Kendall's tau matrix is block-structured with constant values in each off-diagonal block, this function estimates Kendall's tau matrix “fast”, i.e. in time N n log(n), where N is the amount of pairs that are averaged.

Usage

KTMatrixEst(dataMatrix, blockStructure = NULL, averaging = "no")

Arguments

dataMatrix

matrix of size (n,d) containing n observations of a d-dimensional random vector.

blockStructure

list of vectors. Each vector corresponds to one group of variables and contains the indexes of the variables that belongs to this group. blockStructure must be a partition of 1:d, where d is the number of columns in dataMatrix.

averaging

type of averaging used for fast estimation. Possible choices are

• no: no averaging;

• all: averaging all Kendall's taus in each block. N is then the number of entries in the block, i.e. the products of both dimensions.

• diag: averaging along diagonal blocks elements. N is then the minimum of the block's dimensions.

• row: averaging Kendall's tau along the smallest block side. N is then the minimum of the block's dimensions.

Value

matrix with dimensions depending on averaging.

• If averaging = no, the function returns a matrix of dimension (n,n) which estimates the Kendall's tau matrix.

• Else, the function returns a matrix of dimension (length(blockStructure) , length(blockStructure)) giving the estimates of the Kendall's tau for each block with ones on the diagonal.

Author(s)

Rutger van der Spek, Alexis Derumigny

Examples

# Estimating off-diagonal block Kendall's taus
matrixCov = matrix(c(1  , 0.5, 0.3 ,0.3,
                     0.5,   1, 0.3, 0.3,
                     0.3, 0.3,   1, 0.5,
                     0.3, 0.3, 0.5,   1), ncol = 4 , nrow = 4)
dataMatrix = mvtnorm::rmvnorm(n = 100, mean = rep(0, times = 4), sigma = matrixCov)
blockStructure = list(1:2, 3:4)
KTMatrixEst(dataMatrix = dataMatrix, blockStructure = blockStructure,
            averaging = "all")