LearnNonparam

Overview

This R package implements several non-parametric tests in chapters 1-5 of Higgins (2004).

It depends on R6 for object oriented design and Rcpp for integration of R and C++.

Installation

For the latest bug fixes and improvements, please install the development version of this R package using

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

Feedback and contributions are welcome. Please feel free to report bugs or request new features by opening an issue.

Usage

library(LearnNonparam)
options(LearnNonparam.pmt_progress = TRUE)

• Construct a test object

  • from some R6 class directly

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

  • using the pmt (permutation test) wrapper

  # recommended for a unified API
  t <- 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 the two-sample Cramér-Von Mises test as an example:

t <- define_pmt(
    # this is a two-sample permutation test
    inherit = "twosample",
    statistic = function(x, y) {
        # (optional) pre-calculate certain constants that remain invariant during permutation
        n_x <- length(x)
        n_y <- length(y)
        F_x <- seq_len(n_x) / n_x
        G_y <- seq_len(n_y) / n_y
        # return a closure to calculate the test statistic
        function(x, y) {
            x <- sort.int(x)
            y <- sort.int(y)
            F <- approxfun(x, F_x, "constant", 0, 1, ties = "ordered")
            G <- approxfun(y, G_y, "constant", 0, 1, ties = "ordered")
            sum(c(F_x - G(x), G_y - F(y))^2)
        }
    },
    # reject the null hypothesis when the test statistic is large
    rejection = "r",
    scoring = "none", n_permu = 1e4,
    name = "Two-Sample Cramér-Von Mises Test",
    alternative = "samples are from different continuous distributions"
)

t$test(rnorm(10), runif(10))$print()

References

Higgins, J. J. 2004. An Introduction to Modern Nonparametric Statistics. Duxbury Advanced Series. Brooks/Cole. https://books.google.com.hk/books?id=vhmFQgAACAAJ.