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multivariance (version 2.4.1)

Measuring Multivariate Dependence Using Distance Multivariance

Description

Distance multivariance is a measure of dependence which can be used to detect and quantify dependence of arbitrarily many random vectors. The necessary functions are implemented in this packages and examples are given. It includes: distance multivariance, distance multicorrelation, dependence structure detection, tests of independence and copula versions of distance multivariance based on the Monte Carlo empirical transform. Detailed references are given in the package description, as starting point for the theoretic background we refer to: B. Bttcher, Dependence and Dependence Structures: Estimation and Visualization Using the Unifying Concept of Distance Multivariance. Open Statistics, Vol. 1, No. 1 (2020), .

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Install

install.packages('multivariance')

Monthly Downloads

248

Version

2.4.1

License

GPL-3

Maintainer

Bj<c3><b6>rn B<c3><b6>ttcher

Last Published

October 6th, 2021

Functions in multivariance (2.4.1)

Computes the explicit coefficients for the finite sample variance for a sample of size N

dependence example: k-independent coin sampling

computes the doubly centered distance matrices

cleanup dependence structure graph

copula.multicorrelation

coupla versions of distance multicorrelation

computes a doubly centered distance matrix

circle.coordinates

calculates the coordinates of n points on a circle of radius r if only 1 inner point, then it is placed in the center

computes the doubly centered distance matrices, mus and bcds

anscombe.extended

Extended Anscombe's Quartett

given the sample of a single variable the doubly centered distance matrix, mu (the limit moments) and bcd (the terms for the finite sample moments) are computed

dependence.structure.full

functions to detect the full (without clustering) dependence structure

dep_struct_iterated_13_100

example dataset for dependence.structure

doubleCenterBiasCorrected

bias corrected double centering # included for speed comparison

double centering of a matrix

functions which are required for the calculation of the finite sample expectation and variance for m-multivariance and total multivariance

transforms a distance matrix to a matrix

dep_struct_several_26_100

example dataset for dependence.structure

check if lower order dependencies are present for the given tuple indices here 'm.values' is a list of boolean matrices. Matrix [[k]] corresponds to the k tuples. For each number of tuples, the first columns of the matrix always contain the indices of the tuples

for the fast detection of the full dependence structure

doubleCenterBiasCorrectedUpper

bias corrected double centering with normalizing # included for speed comparison

dep_struct_ring_15_100

example dataset for dependence.structure

doubleCenterBiasCorrectedUpperLower

bias corrected double centering with normalizing constants for upper and lower bound

copula.multicorrelation.test

independence tests using the copula versions of distance multivariance

copula.multivariance

copula version of distance multivariance

cluster detection

dep_struct_star_9_100

example dataset for dependence.structure

Returns the row indices of matrix A which match with B Use the fast cpp implementation 'match_rows' instead. Function here just for reference.

A dependent Monte Carlo emprical transform

layout_on_circles

special igraph layout for the dependence structure visualization

list of distance matrices

m.multivariance

m distance multivariance

distance matrix

is.doubly.centered

checks if a matrix is doubly centered

multivariances.all

simultaneous computation of multivariance and total/ 2-/ 3-multivariance

pairwise.multicorrelation.bias.corrected

pairwise multicorrelation

multivariance.timing

estimate of the computation time

dependence.structure

determines the dependence structure

p.value.to.star.label

transforms a p-value into the corresponding label

Transform a vector of samples into a vector of samples of the uniform distribution such that, if applied to multiple (dependent) sample vectors, the dependence is preserved.

multicorrelation

distance multicorrelation

multicorrelation.bias.corrected

bias corrected total multicorrelations

multivariance.pvalue

transform multivariance to p-value

independence.test

test for independence

fastEuclideanCdm

fast centered Euclidean distance matrix

doubleCenterSymMat

double center a symmetric matrix

Monte Carlo empirical transform

multivariance.test

independence tests based on (total-/2-/3-) multivariance

rejection.level

rejection level for the test statistic

approximate distribution function of a Gaussian quadratic form

resample the columns of a matrix

simple.int.hash

Simple integer hash from text

sums.of.products

This is the function GC which is required for the computation of the finite sample variance for m and total multivariance

multivariance-package

multivariance: Measuring Multivariate Dependence Using Distance Multivariance

resample.rejection.level

rejection level via resampling

distance multivariance

resamples doubly centered distance matrices

fast Euclidean distance matrix

sign preserving square root

given the distance matrix the unbiased estimate for mu3 is computed

resample.multivariance

resampling (total /m-) multivariance

moments.for.pearson

computes the moments as required for Pearson's approximation

resample.pvalue

p-value via resampling

pearson.pvalue.unif

compute the p-value by Pearson's approximation assuming uniform marginals and euclidean distance

dependence example: tetrahedron sampling

fast p-value approximation

total.multicorrelation.bias.corrected.upper

# included for speed. it is faster than upper.lower

total.multivariance

total distance multivariance