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This R package implements several non-parametric tests in chapters 1-5ofHiggins (2004), including tests for one sample, twosamples, k samples, paired comparisons, blocked designs, trends andassociation. Built withRcppfor efficiency andR6 forflexible, object-oriented design, it provides a unified framework forperforming or creating custom permutation tests.

Install the stable version fromCRAN:

install.packages("LearnNonparam")

Install the development version fromGithub:

# install.packages("remotes")remotes::install_github("qddyy/LearnNonparam")

library(LearnNonparam)

• Construct a test object

  • from some R6 class directly

  t<-Wilcoxon$new(n_permu=1e6)

  • using thepmt (permutationtest) wrapper

  # recommended for a unified APIt<- pmt("twosample.wilcoxon",n_permu=1e6)

• Provide it with samples

  set.seed(-1)t$test(rnorm(10,1), rnorm(10,0))

  

• Check the results

  t$statistic

  

  t$p_value

  

  options(digits=3)t$print()

  

  ggplot2::theme_set(ggplot2::theme_minimal())t$plot(style="ggplot2",binwidth=1)

  

• Modify some settings and observe the change

  t$type<-"asymp"t$p_value

  

define_pmt allows users to define new permutation tests. Take thetwo-sample Wilcoxon test as an example:

t_custom<- define_pmt(# this is a two-sample permutation testinherit="twosample",statistic=function(x,y) {# (optional) pre-calculate certain constants that remain invariant during permutationm<- length(x)n<- length(y)# return a closure to calculate the test statisticfunction(x,y) sum(x)/m- sum(y)/n    },# reject the null hypothesis when the test statistic is too large or too smallrejection="lr",n_permu=1e5)

Also, the statistic can be written in C++. Leveraging Rcpp sugars andC++14 features, only minor modifications are needed to make itcompatible with C++ syntax.

t_cpp<- define_pmt(inherit="twosample",rejection="lr",n_permu=1e5,statistic="[](const auto& x, const auto& y) {        auto m = x.length();        auto n = y.length();        return [=](const auto& x, const auto& y) {            return sum(x) / m - sum(y) / n;        };    }")

It’s easy to check thatt_custom andt_cpp are equivalent:

x<- rnorm(10,mean=0)y<- rnorm(10,mean=5)

set.seed(0)t_custom$test(x,y)$print()

set.seed(0)t_cpp$test(x,y)$print()

coin is a commonly used Rpackage for performing permutation tests. Below is a benchmark:

library(coin)data<- c(x,y)group<-factor(c(rep("x", length(x)), rep("y", length(y))))options(LearnNonparam.pmt_progress=FALSE)benchmark<-microbenchmark::microbenchmark(R=t_custom$test(x,y),Rcpp=t_cpp$test(x,y),coin= wilcox_test(data~group,distribution= approximate(nresample=1e5,parallel="no")))

benchmark

It can be seen that C++ brings significantly better performance thanpure R, even surpassing thecoin package (under sequential execution).However, all tests in this package are currently written in R with noplans for migration to C++ in the future. This is because the primarygoal of this package is not to maximize performance but to offer aflexible framework for permutation tests.