h.alpha.n: Compute h, the subsample size for MCD and LTS In robustbase: Basic Robust Statistics

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

 `1` ```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.

`covMcd` and `ltsReg` which are defined by h = h(α,n,p) and hence both use `h.alpha.n`.
 ```1 2 3 4 5 6 7 8``` ```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)) ```