serrlog_sf: Squared error log scoring function

In scoringfunctions: A Collection of Loss Functions for Assessing Point Forecasts

Squared error log scoring function

Description

The function serrlog_sf computes the squared error log scoring function when y materialises and x is the \exp(\textnormal{E}_F[\log(Y)]) predictive functional.

The squared error log scoring function is defined in Houghton-Carr (1999).

Usage

serrlog_sf(x, y)

Arguments

x	Predictive \exp(\textnormal{E}_F[\log(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 squared error scoring function is defined by:

S(x, y) := (\log(x) - \log(y))^2

Domain of function:

x > 0

y > 0

Range of function:

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

Value

Vector of squared errors of log-transformed variables.

Note

For details on the squared error log scoring function, see Houghton-Carr (1999).

The squared error log scoring function is negatively oriented (i.e. the smaller, the better).

The squared error log scoring function is strictly \mathbb{F}-consistent for the \exp(\textnormal{E}_F[\log(Y)]) functional. \mathbb{F} is the family of probability distributions F for which \textnormal{E}_F[\log(Y)] exists and is finite (Tyralis and Papacharalampous 2025).

References

Houghton-Carr HA (1999) Assessment criteria for simple conceptual daily rainfall-runoff models. Hydrological Sciences Journal 44(2):237–261. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/02626669909492220")}.

Tyralis H, Papacharalampous G (2025) Transformations of predictions and realizations in consistent scoring functions. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.48550/arXiv.2502.16542")}.

Examples

# Compute the squarer error log scoring function.

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

df$squaredlog_error <- serrlog_sf(x = df$x, y = df$y)

print(df)

scoringfunctions documentation built on April 4, 2025, 12:28 a.m.