capping_function: Capping function

In scoringfunctions: A Collection of Loss Functions for Assessing Point Forecasts

Capping function

Description

The function capping_function computes the value of the capping function, defined in Taggart (2022), p.205.

It is used by the generalized Huber loss function among others (see Taggart 2022).

Usage

capping_function(t, a, b)

Arguments

t	It can be a vector of length n.
a	It can be a vector of length n (must have the same length as t).
b	It can be a vector of length n (must have the same length as t).

Details

The capping function \kappa_{a,b}(t) is defined by:

\kappa_{a,b}(t) := \max \lbrace \min \lbrace t,b \rbrace, -a \rbrace

or equivalently,

\kappa_{a,b}(t) := \left\{ \begin{array}{ll} -a, & t \leq -a\\ t, & -a < t \leq b\\ b, & t > b \end{array} \right.

Domain of function:

t \in \mathbb{R}

a \geq 0

b \geq 0

Value

Vector of values of the capping function.

Note

For the definition of the capping function, see Taggart (2022), p.205.

References

Taggart RJ (2022) Point forecasting and forecast evaluation with generalized Huber loss. Electronic Journal of Statistics 16:201–231. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/21-EJS1957")}.

Examples

# Compute the capping function.

df <- data.frame(
    t = c(1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 2.5, 2.5, 3.5, 3.5),
    a = c(0, 0, 0, 0, Inf, Inf, Inf, Inf, 2, 3, 2, 3, 2, 3),
    b = c(0, 0, Inf, Inf, 0, 0, Inf, Inf, 3, 2, 3, 2, 3, 2)
)

df$cf <- capping_function(t = df$t, a = df$a, b = df$b)

print(df)

scoringfunctions documentation built on April 4, 2025, 12:28 a.m.