scoringfunctions (version 1.1)

serrsq_sf: Squared error of squares scoring function

Description

The function serrsq_sf computes the squared error of squares scoring function when \(y\) materialises and \(x\) is the \(\sqrt{\textnormal{E}_F[Y^2]}\) predictive functional.

The squared error of squares scoring function is defined in Thirel et al. (2024).

Usage

serrsq_sf(x, y)

Value

Vector of squared errors of squared-transformed variables.

Arguments

x

Predictive \(\sqrt{\textnormal{E}_F[Y^2]}\) 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 of squares scoring function is defined by:

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

Domain of function:

$$x \geq 0$$

$$y \geq 0$$

Range of function:

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

References

Thirel G, Santos L, Delaigue O, Perrin C (2024) On the use of streamflow transformations for hydrological model calibration. Hydrology and Earth System Sciences 28(21):4837--4860. tools:::Rd_expr_doi("10.5194/hess-28-4837-2024").

Tyralis H, Papacharalampous G (2025) Transformations of predictions and realizations in consistent scoring functions. tools:::Rd_expr_doi("10.48550/arXiv.2502.16542").

Examples

# Compute the squarer error of squares scoring function.

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

df$squaredsq_error <- serrsq_sf(x = df$x, y = df$y)

print(df)