scoringfunctions (version 1.1)

obsweighted_sf: Observation-weighted scoring function

Description

The function obsweighted_sf computes the observation-weighted scoring function when \(y\) materialises and \(x\) is the predictive \(\dfrac{\textnormal{E}_F [Y^{2}]}{\textnormal{E}_F [Y]}\) functional.

The observation-weighted scoring function is defined in p. 752 in Gneiting (2011).

Usage

obsweighted_sf(x, y)

Value

Vector of observation-weighted errors.

Arguments

x

Predictive \(\dfrac{\textnormal{E}_F [Y^{2}]}{\textnormal{E}_F [Y]}\) 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 observation-weighted scoring function is defined by:

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

Domain of function:

$$x > 0$$

$$y > 0$$

Range of function:

$$S(x, y) \geq 0, \forall x, y > 0$$

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").

Examples

# Compute the observation-weighted scoring function.

df <- data.frame(
    y = rep(x = 2, times = 3),
    x = 1:3
)

df$squared_relative_error <- obsweighted_sf(x = df$x, y = df$y)

print(df)