hhg.example.datagen: A set of example data generators used to demonstrate the HHG...

In HHG: Heller-Heller-Gorfine Tests of Independence and Equality of Distributions

Description

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.

Usage

hhg.example.datagen(n, example)

Arguments

n	The desired sample size
example	The choice of example

Value

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.

Author(s)

Shachar Kaufman and Ruth Heller

References

Newton, M.A. (2009). Introducing the discussion paper by Szekely and Rizzo. Annals of applied statistics, 3 (4), 1233-1235.

Examples

X = hhg.example.datagen(50, 'Diamond')
plot(X[1,], X[2,])

X = hhg.example.datagen(50, 'FourClassUniv')
plot(X)

Example output

HHG Ver. 2.3.2 - package for non parametric tests of independence and equality of distributions.
type vignette('HHG') or ?HHG for documentation, examples and a quickstart guide.
use suppressPackageStartupMessages(library(HHG)) to suppress this message.

HHG documentation built on May 15, 2021, 9:06 a.m.