qad {qad}R Documentation

Measure of (asymmetric and directed) dependence

Description

Quantification of (asymmetric and directed) dependence structures between two random variables X and Y.

Usage

qad(x, ...)

## S3 method for class 'data.frame'
qad(
  x,
  resolution = NULL,
  permutation = FALSE,
  nperm = 1000,
  DoParallel = TRUE,
  registerC = registerDoParallel,
  ncores = NULL,
  print = TRUE,
  remove.00 = FALSE,
  ...
)

## S3 method for class 'numeric'
qad(
  x,
  y,
  resolution = NULL,
  permutation = FALSE,
  nperm = 1000,
  DoParallel = TRUE,
  registerC = registerDoParallel,
  ncores = NULL,
  print = TRUE,
  remove.00 = FALSE,
  ...
)

Arguments

x

a data.frame containing two columns with the observations of the bivariate 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 emp_c_copula). Default = NULL uses the optimal resolution.

permutation

a logical indicating whether a p-value (based on permutations) is computed; otherwise a p-value is computed on MC-simulations (see pqad()).

nperm

an integer indicating the number of permutation runs.

DoParallel

a logical value indicating whether the repetitions in the permutation test is computed parallel.

registerC

function to register the parallel environment. It is recommended to use registerDoParallel(), contained in the doParallel package (default). Another option, especially for a linux based system, is to install the doMC package and use registerDoMC

ncores

an integer indicating the number of cores used for parallel computation. (Default = NULL, which is defined by max(cores)-1)

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.

Details

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 (ECB), and calculate zeta_1 of the ECB copula and its transpose. In order to test for independence (in both directions), the distribution (and hence the p-value) of a Monte-Carlo simulation is provided (default). Alternatively, a permutation test can be used to obtain p-values for the direction and asymmetry.

Value

qad returns an object of class qad containing the following components:

data

a data.frame containing the input data.

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.

Note

The computation of the p-values (aggregated by permutations) take some time.

References

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.

Examples

#Example 1 (independence)

n <- 1000
x <- runif(n,0,1)
y <- runif(n,0,1)
sample <- data.frame(x,y)
qad(sample)

###

#Example 2 (mutual complete dependence)

n <- 1000
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)

[Package qad version 0.2.0 Index]