zeta1: Multivariate dependence measure

View source: R/zeta1.R

zeta1R Documentation

Multivariate dependence measure

Description

Function for estimating the non-parametric copula-based multivariate measure of dependence ΞΆ1. This measure quantifies the extent of dependence between a d-dimensional random vector X and a uni-variate random variable y (i.e., it measures the influence of d explanatory variables X1,...,Xd on a univariate variable y).

Usage

zeta1(X, y, ties.correction = FALSE, bin.size = "fixed", resolution = NULL)

Arguments

X

a numeric matrix or data.frame of dimension d containing the explanatory variables

y

a numeric vector containing the uni-variate response variable

ties.correction

logical indicating if the measure of dependence should be calculated with ties-correction (experimental version). Default = FALSE.

bin.size

either "fixed", "adaptive" or "sparse.adaptive", indicating whether the checkerboard copula may vary its bin sizes (defaults to "fixed"). Setting this to "adaptive" might affect the results but will be faster if the sample has many ties.

resolution

an integer indicating the resolution N of the checkerboard aggregation. We recommend to use the default configuration (resolution = NULL), which uses the resolution N(n) = floor(n^(1/(d+1))), where d denotes the number of explanatory variables.

Details

see function qmd(...).

Value

A numeric value indicating the extent of dependence between the vector X and the variable y (or, equivalently, the influence of X on y).

References

Griessenberger, F., Junker, R.R. and Trutschnig, W. (2022). On a multivariate copula-based dependence measure and its estimation, Electronic Journal of Statistics, 16, 2206-2251.

Examples

#(complete dependence for dimension 4)
n <- 300
x1 <- runif(n)
x2 <- runif(n)
x3 <- x1 + x2 + rnorm(n)
y <- x1 + x2 + x3
zeta1(X = cbind(x1,x2,x3), y = y)

#(independence for dimension 4)
n <- 500
x1 <- runif(n)
x2 <- runif(n)
x3 <- x1 + x2 + rnorm(n)
y <- runif(n)
zeta1(X = cbind(x1,x2,x3), y = y)

#(binary output for dimension 3)
n <- 500
x1 <- runif(n)
x2 <- runif(n)
y <- ifelse(x1 + x2 < 1, 0, 1)
zeta1(X = cbind(x1,x2), y = y)

qmd documentation built on Aug. 22, 2022, 5:07 p.m.

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