qad | R Documentation |
Quantification of (asymmetric and directed) dependence structures between two random variables X and Y.
qad(x, ...) ## S3 method for class 'data.frame' qad( x, resolution = NULL, p.value = TRUE, nperm = 1000, p.value_asymmetry = FALSE, nboot = 1000, print = TRUE, remove.00 = FALSE, ... ) ## S3 method for class 'numeric' qad( x, y, resolution = NULL, p.value = TRUE, nperm = 1000, p.value_asymmetry = FALSE, nboot = 1000, print = TRUE, remove.00 = FALSE, ... )
x |
a data.frame containing two columns with the observations of the bi-variate sample or a (non-empty) numeric vector of data values |
... |
Further arguments passed to 'qad' will be ignored |
resolution |
an integer indicating the number of strips for the checkerboard aggregation (see ECBC). We recommend to use the default value (resolution = NULL) |
p.value |
a logical indicating whether to return a p-value of rejecting independence (based on permutation). |
nperm |
an integer indicating the number of permutation runs (if p.value = TRUE) |
p.value_asymmetry |
a logical indicating whether to return a (heuristic) p-value for the measure of asymmetry (based on bootstrap). |
nboot |
an integer indicating the number of runs for the bootstrap. |
print |
a logical indicating whether the result of qad is printed. |
remove.00 |
a logical indicating whether double 0 entries should be excluded (default = FALSE) |
y |
a (non-empty) numeric vector of data values. |
qad is the implementation of a strongly consistent estimator of the copula based dependence measure zeta_1 introduced in Trutschnig 2011. We first compute the empirical copula of a two-dimensional sample, aggregate it to the so called empirical checkerboard copula (ECBC), and calculate zeta_1 of the ECBC and its transpose. In order to test for independence (in both directions), a built-in p-value is implemented (a permutation test with nperm permutation runs to estimate the p-value). Furthermore, a (heuristic) bootstrap test with nboot runs can be applied to estimate a p-value for the measure of asymmetry a.
qad returns an object of class qad containing the following components:
data |
a data.frame containing the input data. |
q(X,Y) |
influence of X on Y |
q(Y,X) |
influence of Y on X |
max.dependence |
maximal dependence |
results |
a data.frame containing the results of the dependence measures. |
mass_matrix |
a matrix containing the mass distribution of the empirical checkerboard copula. |
resolution |
an integer containing the used resolution of the checkerboard aggregation. |
n |
Sample size. |
Trutschnig, W. (2011). On a strong metric on the space of copulas and its induced dependence measure, Journal of Mathematical Analysis and Applications 384, 690-705.
Junker, R., Griessenberger, F. and Trutschnig, W. (2021). Estimating scale-invariant directed dependence of bivariate distributions. Computational Statistics and Data Analysis, 153.
A tutorial can be found at http://www.trutschnig.net/software.html.
#Example 1 (independence) n <- 100 x <- runif(n,0,1) y <- runif(n,0,1) sample <- data.frame(x,y) qad(sample) ### #Example 2 (mutual complete dependence) n <- 500 x <- runif(n,0,1) y <- x^2 sample <- data.frame(x,y) qad(sample) #Example 3 (complete dependence) n <- 1000 x <- runif(n,-10,10) y <- sin(x) sample <- data.frame(x,y) qad(sample) #Example 4 (Asymmetry) n <- 100 x <- runif(n,0,1) y <- (2*x) %% 1 qad(x, y)
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