Six examples (Circle, Diamond, Parabola, 2Parabolas, W, 4indclouds) are taken from Newton's introduction to the discussion of the Energy Test in The Annals of Applied Statistics (2009). These are simple univariate dependence structures (or independence, in the latter case) used to demonstrate the tests of independece. The remaining examples (TwoClassUniv, FourClassUniv, TwoClassMultiv) generate data suitable for demonstrating the k-sample test (and in particular, the two-sample test).
It has been pointed out by Pierre Lafaye de Micheaux (private correspondence) that sampling should replace equidistant points in the data generation functions of the 2Parabolas, W, and Circle relationships (i.e., use x = runif(n, -1, 1) instead of x = seq(-1, 1, length = n)). The power resulting from this modification is close to the original power. We did not implement this change in order to preserve the reproducibility of the results reported in paper " A consistent multivariate test of association based on ranks of distances", Biometrika (2016) 103 (1): 35-47.
One can see HHG::hhg.example.datagen and HHG:::.datagenW (for example) for the source code for the data generation procedure.
hhg.example.datagen(n, example)For example in {Circle, Diamond, Parabola, 2Parabolas, W, and 4indclouds}, a matrix of two rows is returned, one row per variable. Columns are i.i.d. samples. Given these data, we would like to test whether the two variables are statistically independent. Except for the 4indclouds case, all examples in fact have variables that are dependent.
When example is one of {TwoClassUniv, FourClassUniv, TwoClassMultiv}, a list is returned with elements x and y. y is a vector with values either 0 or 1 (for TwoClassUniv and TwoClassMultiv) or in 0:3 for (for FourClassUniv). x is a real valued random variable (TwoClassUniv and FourClassUniv) or vector (TwoClassMultiv) which is not independent of y.
The desired sample size
The choice of example
Shachar Kaufman and Ruth Heller
Newton, M.A. (2009). Introducing the discussion paper by Szekely and Rizzo. Annals of applied statistics, 3 (4), 1233-1235.
X = hhg.example.datagen(50, 'Diamond')
plot(X[1,], X[2,])
X = hhg.example.datagen(50, 'FourClassUniv')
plot(X)
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