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

Description Usage Arguments Value See Also Examples

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

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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.

See Also

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

Examples

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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))


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