argmin.HT.LOO: Perform argmin hypothesis test.

In argminCS: Argmin Inference over a Discrete Candidate Set

Perform argmin hypothesis test.

Description

Test if a dimension may be argmin, using the LOO (leave-one-out) algorithm in Zhang et al 2024.

Usage

argmin.HT.LOO(
  difference.matrix,
  sample.mean = NULL,
  min.algor = "softmin",
  lambda = NULL,
  const = 2.5,
  enlarge = TRUE,
  alpha = 0.05,
  true.mean.difference = NULL,
  output.weights = FALSE,
  scale.input = TRUE,
  seed = NULL,
  ...
)

Arguments

difference.matrix	A n by (p-1) difference data matrix (reference dimension - the rest); each of its row is a (p-1)-dimensional vector of differences.
sample.mean	The sample mean of differences; defaults to NULL. It can be calculated via colMeans(difference.matrix).
min.algor	The algorithm to compute the test statistic by weighting across dimensions; 'softmin' uses exponential weighting, while 'argmin' picks the largest mean coordinate directly. Defaults to 'softmin'.
lambda	The real-valued tuning parameter for exponential weightings (the calculation of softmin); defaults to NULL. If lambda=NULL (recommended), the function would determine a lambda value in a data-driven way.
const	The scaling constant for initial data-driven lambda
enlarge	A boolean value indicating if the data-driven lambda should be determined via an iterative enlarging algorithm; defaults to TRUE.
alpha	The significance level of the hypothesis test; defaults to 0.05.
true.mean.difference	The population mean of the differences. (Optional); used to compute a centered test statistic for simulation or diagnostic purposes.
output.weights	A boolean variable specifying whether the exponential weights should be outputted; defaults to FALSE.
scale.input	A boolean variable specifying whether the input difference matrix should be standardized. Defaults to TRUE
seed	(Optional) If provided, used to seed the random sampling (for reproducibility).
...	Additional arguments to lambda.adaptive.enlarge, is.lambda.feasible.LOO.

Value

A list containing:

test.stat.scale	The scaled test statistic
critical.value	The critical value for the hypothesis test. Being greater than it leads to a rejection.
std	The standard deviation estimate.
ans	A character string: either 'Reject' or 'Accept', depending on the test outcome.
lambda	The lambda used in the hypothesis testing.
lambda.capped	Boolean variable indicating the data-driven lambda has reached the large threshold n^5
residual.slepian	The final approximate first order stability term for the data-driven lambda.
variance.bound	The final variance bound for the data-driven lambda.
test.stat.centered	(Optional) The centered test statistic, computed only if true.mean.difference is provided.
exponential.weights	(Optional) A (n by p-1) matrix storing the exponential weightings in the test statistic.

argminCS documentation built on Aug. 8, 2025, 7:51 p.m.