Test if a dimension may be argmin, using the LOO (leave-one-out) algorithm in Zhang et al 2024.
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,
...
)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. |
A n by (p-1) difference data matrix (reference dimension - the rest); each of its row is a (p-1)-dimensional vector of differences.
The sample mean of differences; defaults to NULL. It can be calculated via colMeans(difference.matrix).
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'.
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.
The scaling constant for initial data-driven lambda
A boolean value indicating if the data-driven lambda should be determined via an iterative enlarging algorithm; defaults to TRUE.
The significance level of the hypothesis test; defaults to 0.05.
The population mean of the differences. (Optional); used to compute a centered test statistic for simulation or diagnostic purposes.
A boolean variable specifying whether the exponential weights should be outputted; defaults to FALSE.
A boolean variable specifying whether the input difference matrix should be standardized. Defaults to TRUE
(Optional) If provided, used to seed the random sampling (for reproducibility).
Additional arguments to lambda.adaptive.enlarge, is.lambda.feasible.LOO.