aerr_sf {scoringfunctions}

Absolute error scoring function

Description

The function aerr_sf computes the absolute error scoring function when y materializes 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)

Arguments

x

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

y

Realization (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 \R

y \in \R

Range of function:

S(x, y) \geq 0, \forall x, y \in \R

Value

Vector of absolute errors.

Note

For details on the absolute error scoring function, see Gneiting (2011).

The median functional is the median of the probability distribution F of y (Gneiting 2011).

The absolute error scoring function is negatively oriented (i.e. the smaller, the better).

The absolute error scoring function is strictly consistent for the median functional relative to the family \mathbb{F} of potential probability distributions F for the future y for which the first moment exists and is finite (Thomson 1979, Saerens 2000, Gneiting 2011).

References

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

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

Thomson W (1979) Eliciting production possibilities from a well-informed manager. Journal of Economic Theory 20(3):360–380. 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)