serrpower_sf {scoringfunctions} | R Documentation |
Squared error of power transformations scoring function
Description
The function serrpower_sf computes the squared error of power transformations
scoring function when y
materialises and x
is the
(\textnormal{E}_F[Y^a])^{(1/a)}
predictive functional.
The squared error of power transformations scoring function is defined in Tyralis and Papacharalampous (2025).
Usage
serrpower_sf(x, y, a)
Arguments
x |
Predictive |
y |
Realisation (true value) of process. It can be a vector of length
|
a |
It can be a vector of length |
Details
The squared error of power transformations scoring function is defined by:
S(x, y) := (x^a - y^a)^2
Domain of function:
Case #1
a > 0
x \geq 0
y \geq 0
Case #2
a \neq 0
x > 0
y > 0
Range of function:
S(x, y) \geq 0, \forall x, y, a
Value
Vector of squared errors of power-transformed variables.
Note
For details on the squared error of power tranformations scoring function, see Tyralis and Papacharalampous (2025).
The squared error of power tranformations scoring function is negatively oriented (i.e. the smaller, the better).
The squared error of power transformations scoring function is strictly
\mathbb{F}
-consistent for the (\textnormal{E}_F[Y^a])^{(1/a)}
functional. \mathbb{F}
is the family of probability distributions F
for which \textnormal{E}_F[Y^a]
exists and is finite (Tyralis and
Papacharalampous 2025).
References
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 power tranformations scoring function.
df <- data.frame(
y = rep(x = 2, times = 3),
x = 1:3,
a = 1:3
)
df$squaredpower_error <- serrpower_sf(x = df$x, y = df$y, a = df$a)
print(df)