CS.argmin: Construct a discrete confidence set for argmin.

In argminCS: Argmin Inference over a Discrete Candidate Set

Construct a discrete confidence set for argmin.

Description

This is a wrapper to construct a discrete confidence set for argmin. Multiple methods are supported.

Usage

CS.argmin(data, method = "softmin.LOO", alpha = 0.05, ...)

Arguments

data	A n by p data matrix; each row is a p-dimensional sample.
method	A string indicating the method used to construct the confidence set. Defaults to 'softmin.LOO'. Can be abbreviated (e.g., 'SML' for 'softmin.LOO'). See **Details** for available methods and abbreviations.
alpha	The significance level; defaults to 0.05. The function produces a 1 - \alpha confidence set.
...	Additional arguments to argmin.HT.LOO, lambda.adaptive.enlarge, is.lambda.feasible.LOO, argmin.HT.MT, argmin.HT.gupta. A correct argument name needs to be specified if it is used.

Details

The supported methods include:

softmin.LOO (SML)	Leave-one-out algorithm using exponential weighting. Proposed by \insertRefzhang2024winnersargminCS.
argmin.LOO (HML)	A variant of SML that uses hard argmin instead of exponential weighting. Not recommended.
nonsplit (NS)	A variant of SML without data splitting. Requires a fixed lambda value as an additional argument. Not recommended
Bonferroni (MT)	Multiple testing using Bonferroni correction.
Gupta (GTA)	The method proposed by \insertCitegupta.1965;textualargminCS. Requires independence and the same population standard deviation for all dimensions.
Futschik (FCHK)	A two-step method from \insertCitefutschik.1995;textualargminCS. Requires independence and the same population standard deviation for all dimensions.

Value

A vector of indices (1-based) representing the (1 - alpha) confidence set.

References

\insertRef

zhang2024winnersargminCS

\insertRef

cck.many.momentsargminCS

\insertRef

gupta.1965argminCS

\insertRef

futschik.1995argminCS

Examples

r <- 4
n <- 200
mu <- (1:20)/20
cov <- diag(length(mu))
set.seed(108)
data <- MASS::mvrnorm(n, mu, cov)
sample.mean <- colMeans(data)

## softmin.LOO
CS.argmin(data)

## use seed
CS.argmin(data, seed=13)

## argmin.LOO
CS.argmin(data, method='HML')

## nonsplit
CS.argmin(data, method='NS', lambda=sqrt(n)/2.5)

## Bonferroni (choose t test because of normal data)
CS.argmin(data, method='MT', test='t')

## Gupta
CS.argmin(data, method='GTA')

## Futschik two-step method
# default alpha.1, alpha.2
CS.argmin(data, method='FCHK')

alpha.1 <- 0.0005
alpha.2 <- 1 - (0.95/(1 - alpha.1))
CS.argmin(data, method='FCHK', alpha.1=0.0005, alpha.2=alpha.2)

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