robustbase: h.alpha.n – R documentation

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h.alpha.n

Compute h, the subsample size for MCD and LTS

Description

Compute h(alpha) which is the size of the subsamples to be used for MCD and LTS. Given alpha, n and p, h is an integer, h ~= alpha*n, where the exact formula also depends on p.

For α = 1/2, h == floor(n+p+1)/2; for the general case, it's simply n2 <- (n+p+1) %/% 2; floor(2*n2 - n + 2*(n-n2)*alpha).

Usage

h.alpha.n(alpha, n, p)

Arguments

`alpha`	fraction, numeric (vector) in [0.5, 1], see, e.g., `covMcd`.
`n`	integer (valued vector), the sample size.
`p`	integer (valued vector), the dimension.

Value

numeric vector of h(α, n,p); when any of the arguments of length greater than one, the usual R arithmetic (recycling) rules are used.

Examples

n <- c(10:20,50,100)
p <- 5
## show the simple "alpha = 1/2" case:
cbind(n=n, h= h.alpha.n(1/2, n, p), n2p = floor((n+p+1)/2))

## alpha = 3/4 is recommended by some authors :
n <- c(15, 20, 25, 30, 50, 100)
cbind(n=n, h= h.alpha.n(3/4, n, p = 6))

robustbase

Basic Robust Statistics

v0.93-7

GPL (>= 2)

Authors

Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Peter Rousseeuw [ctb] (Qn and Sn), Christophe Croux [ctb] (Qn and Sn), Valentin Todorov [aut] (most robust Cov), Andreas Ruckstuhl [aut] (nlrob, anova, glmrob), Matias Salibian-Barrera [aut] (lmrob orig.), Tobias Verbeke [ctb, fnd] (mc, adjbox), Manuel Koller [aut] (mc, lmrob, psi-func.), Eduardo L. T. Conceicao [aut] (MM-, tau-, CM-, and MTL- nlrob), Maria Anna di Palma [ctb] (initial version of Comedian)

Initial release

2021-01-04