argminCS (version 1.1.0)

argmax.HT: A wrapper to perform argmax hypothesis test.

Description

This function performs a hypothesis test to evaluate whether a given dimension may be the argmax. It internally negates the data and reuses the implementation from argmin.HT.

Usage

argmax.HT(data, r = NULL, method = "softmin.LOO", ...)

Value

A character string: 'Accept' or 'Reject', indicating whether the dimension could be an argmax, and relevant statistics.

Arguments

data

(1) A n by p matrix of raw samples (for GTA), or (2) A n by (p-1) difference matrix (for SML, HML, NS, MT). Each row is a sample.

r

The dimension of interest for testing; defaults to NULL. Required for GTA.

method

A string indicating the method to use. Defaults to 'softmin.LOO'. See **Details** for supported methods and abbreviations.

...

Additional arguments passed to argmin.HT.LOO, argmin.HT.MT, argmin.HT.nonsplit, or argmin.HT.gupta.

Details

The supported methods include:

softmin.LOO (SML)	Leave-one-out algorithm using exponential weighting.
argmin.LOO (HML)	A variant of SML that uses hard argmin instead of exponential 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 from gupta.1965argminCS.

References

cck.many.momentsargminCS

gupta.1965argminCS

futschik.1995argminCS

Examples

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

## Define the dimension of interest
r <- 4

## Construct difference matrix for dimension r
difference.matrix.r <- matrix(rep(data[, r], p - 1), ncol = p - 1, byrow = FALSE) - data[, -r]

## softmin.LOO (SML)
argmax.HT(difference.matrix.r)

## use seed
argmax.HT(difference.matrix.r, seed=19)

## With known true difference
true.mean.diff <- mu[r] - mu[-r]
argmax.HT(difference.matrix.r, true.mean = true.mean.diff)

## Without scaling
argmax.HT(difference.matrix.r, scale.input = FALSE)

## With a user-specified lambda
argmax.HT(difference.matrix.r, lambda = sqrt(n) / 2.5)

## Add a seed for reproducibility
argmax.HT(difference.matrix.r, seed = 17)

## argmin.LOO (HML)
argmax.HT(difference.matrix.r, method = "HML")

## nonsplit method
argmax.HT(difference.matrix.r, method = "NS", lambda = sqrt(n)/2.5)

## Bonferroni method (choose t test for normal data)
argmax.HT(difference.matrix.r, method = "MT", test = "t")

## Gupta method (pass full data matrix)
critical.val <- get.quantile.gupta.selection(p = length(mu))
argmax.HT(data, r, method = "GTA", critical.val = critical.val)