meanlog_if: Log-transformed identification function

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

Log-transformed identification function

Description

The function meanlog_if computes the log-transformed identification function, when y materialises and \exp(\textnormal{E}_F[\log(Y)]) is the predictive functional.

The log-transformed identification function is defined in Tyralis and Papacharalampous (2025).

Usage

meanlog_if(x, y)

Arguments

x	Predictive \exp(\textnormal{E}_F[\log(Y)]) functional. 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 mean identification function is defined by:

V(x, y) := \log(x) - \log(y)

Domain of function:

x > 0

y > 0

Range of function:

V(x, y) \in \mathbb{R}, \forall x, y > 0

Value

Vector of values of the log-transformed identification function.

Note

The log-transformed identification function is a strict \mathbb{F}-identification function for the log-transformed expectation \exp(\textnormal{E}_F[\log(Y)]) (Tyralis and Papacharalampous 2025).

\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

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 log-transformed identification function.

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

df$meanlog_if <- meanlog_if(x = df$x, y = df$y)

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