scoringfunctions (version 1.1)

aerr_sf: Absolute error scoring function

Description

The function aerr_sf computes the absolute error scoring function when \(y\) materialises and \(x\) is the predictive median functional.

The absolute error scoring function is defined in Table 1 in Gneiting (2011).

Usage

aerr_sf(x, y)

Value

Vector of absolute errors.

Arguments

x

Predictive median functional (prediction). It can be a vector of length \(n\) (must have the same length as \(y\)).

y

Realisation (true value) of process. It can be a vector of length \(n\) (must have the same length as \(x\)).

Details

The absolute error scoring function is defined by:

$$S(x, y) := |x - y|$$

Domain of function:

$$x \in \mathbb{R}$$

$$y \in \mathbb{R}$$

Range of function:

$$S(x, y) \geq 0, \forall x, y \in \mathbb{R}$$

References

Ferguson TS (1967) Mathematical Statistics: A Decision-Theoretic Approach. Academic Press, New York.

Gneiting T (2011) Making and evaluating point forecasts. Journal of the American Statistical Association 106(494):746--762. tools:::Rd_expr_doi("10.1198/jasa.2011.r10138").

Raiffa H,Schlaifer R (1961) Applied Statistical Decision Theory. Colonial Press, Clinton.

Saerens M (2000) Building cost functions minimizing to some summary statistics. IEEE Transactions on Neural Networks 11(6):1263--1271. tools:::Rd_expr_doi("10.1109/72.883416").

Thomson W (1979) Eliciting production possibilities from a well-informed manager. Journal of Economic Theory 20(3):360--380. tools:::Rd_expr_doi("10.1016/0022-0531(79)90042-5").

Examples

# Compute the absolute error scoring function.

df <- data.frame(
    y = rep(x = 0, times = 5),
    x = -2:2
)

df$absolute_error <- aerr_sf(x = df$x, y = df$y)

print(df)