zeta1 | R Documentation |
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).
zeta1(X, y, ties.correction = FALSE, bin.size = "fixed", resolution = NULL)
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. |
see function qmd(...).
A numeric value indicating the extent of dependence between the vector X and the variable y (or, equivalently, the influence of X on y).
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.
#(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)
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