qad (version 0.1.2)

qad: Measure of (asymmetric) dependence

Description

Quantifies the (asymmetric) dependence structure between two random variables X and Y.

Usage

qad(x, ...)
# S3 method for data.frame
qad(
  x,
  resolution = NULL,
  permutation = FALSE,
  nperm = 100,
  DoParallel = TRUE,
  registerC = registerDoParallel,
  ncores = NULL,
  print = TRUE,
  ...
)
# S3 method for numeric
qad(
  x,
  y,
  resolution = NULL,
  permutation = FALSE,
  nperm = 100,
  DoParallel = TRUE,
  registerC = registerDoParallel,
  ncores = NULL,
  print = TRUE,
  ...
)

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 permutated p-value is computed.

nperm

an integer indicating the number of permutation runs.

DoParallel

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

registerC

function to register the parallel backend. It is recommended to use registerDoParallel() of the doParallel package (default). Another option 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 calculation. Default = NULL uses max(cores)-1

print

a logical indicating whether the result is printed into the console.

y

a (non-empty) numeric vector of data values.

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.

Details

qad is 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 equal dependence in both directions a permutation test based p-value is calculated.

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

# NOT RUN {
#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)
# }