CS.argmin: 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, ...)

Value

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

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 zhang2024winnersargminCS.

`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 gupta.1965;textualargminCS. Requires independence and the same population standard deviation for all dimensions.

`Futschik (FCHK)`	A two-step method from futschik.1995;textualargminCS. Requires independence and the same population standard deviation for all dimensions.

References

zhang2024winnersargminCS cck.many.momentsargminCS gupta.1965argminCS futschik.1995argminCS

Examples

Run this code

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)

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