Beast: Binary Expansion Adaptive Symmetry Test

In BET: Binary Expansion Testing

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
)

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).

Value

Interaction	the most frequent interaction among all subsamples.
BEAST.Statistic	BEAST statistic.
Null.Distribution	simulated null distribution.
p.value	simulated p-value.

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
## Not run: 
  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)

## End(Not run)

BET documentation built on Sept. 11, 2024, 8:14 p.m.