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

In argminCS: Argmin Inference over a Discrete Candidate Set

Construct a discrete confidence set for argmax.

Description

This is a wrapper to construct a confidence set for the argmax by negating the input and reusing CS.argmin.

Usage

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

Arguments

data	An n \times p matrix; each row is a p-dimensional sample.
method	A string indicating the method to use; defaults to 'softmin.LOO'. Can be abbreviated (e.g., 'SML' for 'softmin.LOO'). See Details for full list.
alpha	Significance level. The function returns a 1 - \alpha confidence set.
...	Additional arguments passed to corresponding testing functions.

Details

The supported methods include:

softmin.LOO (SML)	Leave-one-out algorithm using exponential weighting.
argmin.LOO (HML)	Variant of SML that uses hard argmin instead of soft weighting. Not recommended.
nonsplit (NS)	Variant of SML without data splitting. Requires a fixed lambda value. Not recommended.
Bonferroni (MT)	Multiple testing using Bonferroni correction.
Gupta (GTA)	The method of \insertRefgupta.1965argminCS.
Futschik (FCHK)	A two-step method from \insertReffutschik.1995argminCS.

Value

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

References

\insertRef

zhang2024winnersargminCS

\insertRef

gupta.1965argminCS

\insertRef

futschik.1995argminCS

\insertRef

cck.many.momentsargminCS

Examples

set.seed(108)
n <- 200
p <- 20
mu <- (1:p)/p
cov <- diag(p)
data <- MASS::mvrnorm(n, mu, cov)

## softmin.LOO (SML)
CS.argmax(data)

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

## nonsplit (NS) - requires lambda
CS.argmax(data, method = "NS", lambda = sqrt(n)/2.5)

## Bonferroni (MT) - t test default
CS.argmax(data, method = "MT", test = "t")

## Gupta (GTA)
CS.argmax(data, method = "GTA")

## Futschik (FCHK) with default alpha.1 and alpha.2
CS.argmax(data, method = "FCHK")

## Futschik (FCHK) with user-specified alpha.1 and alpha.2
alpha.1 <- 0.001
alpha.2 <- 1 - (0.95 / (1 - alpha.1))
CS.argmax(data, method = "FCHK", alpha.1 = alpha.1, alpha.2 = alpha.2)

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