Formula: F = (1 - eps) Phi + eps H
Usage
Contam(epsilon, H, x = NULL)
Arguments
- epsilon
Contamination fraction in [0, 1).
- H
Sample from the contaminating distribution, used as its
empirical distribution function.
- x
Points at which the mixture cdf is evaluated, or NULL for
-3, -2, ..., 3.
Value
List with estimate (Huber k), k, F,
mean, var, eps, n_H, method.
Details
The gross-error model: a fraction eps of the data comes from an
arbitrary H instead of the nominal normal. The least favourable
member of this neighbourhood has a density normal in the middle and
exponential in the tails, whose score is Huber's psi clipped at k,
where k solves 2 phi(k)/k - 2 Phi(-k) = eps/(1-eps). That k is
reported alongside the mixture itself.
References
Huber (1964), Ann. Math. Statist. 35(1):73-101.
Examples
set.seed(1)
r <- Contam(epsilon = 0.5, H = rnorm(10)); TRUE
#> [1] TRUE
