Nonparametric Hypothesis Testing: Rank and Permutation Methods with Applications in R

Notation and abbreviations

ANOVA: analysis of variance

B: the number of conditional Monte Carlo iterations

∈: belong(s) to

: binomial distribution with n trials and probability θ of success in one trial

CDF: cumulative distribution function

CMC: conditional Monte Carlo

: the correlation operator on (X, Y)

: the covariance operator on (X, Y)

CSP: constrained synchronized permutations

d.f.: degrees of freedom

EDF: empirical distribution function:

: the expectation operator (mean value) of X

: equality in distribution:

: stochastic dominance: and ∃A: F_X(z) < F_Y(z), z ∈ A, with

< ≠ >: means ...