qrmix (version 0.9.0)

Huber: Huber Loss

Description

Evaluates the Huber loss function defined as $$ f(r) = \left\{ \begin{array}{ll} \frac{1}{2}|r|^2 & |r| \le c \\ c(|r|-\frac{1}{2}c) & |r| > c \end{array} \right. $$

$$$$

Usage

Huber(r, c = 1.345)

Arguments

r

a real number or vector.

c

a positive number. If the value is negative, it's absolute value will be used.

Examples

set.seed(1)
x = rnorm(200, mean = 1)
y = Huber(x)
plot(x, y)
abline(h = (1.345)^2/2)