scoringfunctions (version 1.1)

serr_sf: Squared error scoring function

Description

The function serr_sf computes the squared error scoring function when \(y\) materialises and \(x\) is the predictive mean functional.

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

Usage

serr_sf(x, y)

Value

Vector of squared errors.

Arguments

x

Predictive mean 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 squared error scoring function is defined by:

$$S(x, y) := (x - y)^2$$

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

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").

Savage LJ (1971) Elicitation of personal probabilities and expectations. Journal of the American Statistical Association 66(337):783--810. tools:::Rd_expr_doi("10.1080/01621459.1971.10482346").

Examples

# Compute the squarer error scoring function.

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

df$squared_error <- serr_sf(x = df$x, y = df$y)

print(df)