argminCS (version 1.1.0)

CS.argmax: 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, ...)

Value

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

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 gupta.1965argminCS.
Futschik (FCHK)	A two-step method from futschik.1995argminCS.

References

zhang2024winnersargminCS

gupta.1965argminCS

futschik.1995argminCS

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)