serrsq_sf {scoringfunctions} | R Documentation |
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)
Arguments
x |
Predictive |
y |
Realisation (true value) of process. It can be a vector of length
|
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
Value
Vector of squared errors of squared-transformed variables.
Note
For details on the squared error of squares scoring function, see Thirel et al. (2024).
The squared error of squares scoring function is negatively oriented (i.e. the smaller, the better).
The squared error of squares scoring function is strictly
\mathbb{F}
-consistent for the \sqrt{\textnormal{E}_F[Y^2]}
functional. \mathbb{F}
is the family of probability distributions F
for which \textnormal{E}_F[Y^2]
exists and is finite (Tyralis and
Papacharalampous 2025).
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. doi:10.5194/hess-28-4837-2024.
Tyralis H, Papacharalampous G (2025) Transformations of predictions and realizations in consistent scoring functions. 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)