BET (version 0.5.4)

BEAST: Binary Expansion Adaptive Symmetry Test

Description

BEAST (Binary Expansion Adaptive Symmetry Test) is used for nonparametric detection of nonuniformity or dependence.

Usage

BEAST(
  X,
  dep,
  subsample.percent = 1/2,
  B = 100,
  unif.margin = FALSE,
  lambda = NULL,
  index = list(c(1:ncol(X))),
  method = "p",
  num = NULL
)

Value

Interaction

the most frequent interaction among all subsamples.

BEAST.Statistic

BEAST statistic.

Null.Distribution

simulated null distribution.

p.value

simulated p-value.

Arguments

X

a matrix to be tested.

dep

depth of the binary expansion for the BEAST.

subsample.percent

sample size for subsampling.

B

times of subsampling.

unif.margin

logicals. If TRUE the marginal distribution is known to be Uniform[0,1]. Default is FALSE, and empirical cdf transformation will be applied to each marginal distribution.

lambda

tuning parameter for soft-thresholding, default to be \(\sqrt{\log(2^{p \cdot dep}) / (8n)}.\)

index

a list of indices. If provided, test the independence among two or more groups of variables. For example, index = list(c(1,2), c(3))) refers to test the independence between \((X_1, X_2)\) and \(X_3\). Default to be list(c(1:p)) to test if the data follow the multivariate uniform distribution over \([0,1]^p\), where p = ncol(X).

method

If "p", then compute null distribution with permutations. If "s", then compute null distribution with simulations. If "stat", only return interaction and BEAST Statistic. The method = "s" option is only available for testing uniformity and bivariate independence.

num

number of permutations if method == "p" (default to be 100), or simulations if method == "s" (default to be 1000).

Examples

## Elapsed times 7.32 secs
## Measured in R 4.0.2, 32 bit, on a processor 3.3 GHz 6-Core Intel Core i5 under MacOS, 2024/9/6
if (FALSE) {
  x1 = runif(128)
  x2 = runif(128)
  y = sin(4*pi*(x1 + x2)) + 0.8*rnorm(128)
  ##test independence between (x1, x2) and y
  BEAST(cbind(x1, x2, y), 3, index = list(c(1,2), c(3)))
  ##test mutual independence among x1, x2 and y
  BEAST(cbind(x1, x2, y), 3, index = list(1, 2, 3))
  
  ##test bivariate uniformity
  x1 = rbeta(128, 2, 4)
  x2 = rbeta(128, 2, 4)
  BEAST(cbind(x1, x2), 3)
  ##test multivariate uniformity
  x1 = rbeta(128, 2, 4)
  x2 = rbeta(128, 2, 4)
  x3 = rbeta(128, 2, 4)
  BEAST(cbind(x1, x2, x3), 3)
}