h.alpha.n: Compute h, the subsample size for MCD and LTS

In robustbase: Basic Robust Statistics

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 = alpha, n and p, h is an integer, h \approx \alpha n, where the exact formula also depends on p.

For \alpha = 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(\alpha, n,p); when any of the arguments of length greater than one, the usual R arithmetic (recycling) rules are used.

See Also

covMcd and ltsReg which are defined by h = h(\alpha,n,p) and hence both use h.alpha.n.

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 documentation built on Sept. 3, 2025, 3:01 a.m.