Entropy and Testing with np

This vignette is meant to be a small package-side introduction to the entropy-based testing tools in np. It is intentionally much shorter than the legacy article-style document and focuses on what the functions are for and one small runnable example.

The fuller narrative treatment now belongs on the gallery site rather than in a shipped package vignette:

https://jeffreyracine.github.io/gallery/entropy_tests.html

Main functions

The main entropy-based testing functions are:

npdeneqtest: equality of multivariate densities
npunitest: equality of univariate densities
npsymtest: asymmetry in a univariate variable or series
npdeptest: nonlinear pairwise dependence
npsdeptest: nonlinear serial dependence

These functions can be computationally demanding, especially when integration and bootstrap resampling are involved.

A small example

For a first run, it is reasonable to begin with a simple univariate comparison and keep the example small enough that bootstrapping remains practical.

library(np)
#> np 0.70-1
#> Examples and guides at https://jeffreyracine.github.io/gallery/
#> See also vignette("np_getting_started", package = "np")
set.seed(42)

n <- 250
x <- rnorm(n)
y <- rnorm(n)

npunitest(x, y, bootstrap = TRUE)
#> 
#> Consistent Univariate Entropy Density Equality Test
#> 399 Bootstrap Replications
#> 
#> Test Statistic 'Srho': 0.001213156   P Value: 0.98997  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> Fail to reject the null of equality at the 10% level

Practical guidance

start with the smallest example that answers your question,
use the default integral-based versions for serious work unless you have a reason not to,
expect runtime to grow quickly when bootstrap resampling is involved,
if the testing workflow is correct but the runtime becomes burdensome, move to npRmpi rather than rewriting the statistical problem.

Where to go next

?npunitest, ?npdeneqtest, ?npdeptest, ?npsdeptest, ?npsymtest
https://jeffreyracine.github.io/gallery/entropy_tests.html for the longer website article
https://jeffreyracine.github.io/gallery/mpi_large_data.html if the testing workflow is correct but runtime now points to npRmpi