srelerr_sf: Squared relative error scoring function

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

Squared relative error scoring function

Description

The function srelerr_sf computes the squared relative error scoring function when y materialises and x is the predictive \dfrac{\textnormal{E}_F [Y^{2}]}{\textnormal{E}_F [Y]} functional.

The squared relative error scoring function is defined in p. 752 in Gneiting (2011).

Usage

srelerr_sf(x, y)

Arguments

x	Predictive \dfrac{\textnormal{E}_F [Y^{2}]}{\textnormal{E}_F [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 relative error scoring function is defined by:

S(x, y) := ((x - y)/x)^{2}

Domain of function:

x > 0

y > 0

Range of function:

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

Value

Vector of squared relative errors.

Note

For details on the squared relative error scoring function, see Gneiting (2011).

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

The squared relative error scoring function is strictly consistent for the \dfrac{\textnormal{E}_F [Y^{2}]}{\textnormal{E}_F [Y]} functional.

References

Gneiting T (2011) Making and evaluating point forecasts. Journal of the American Statistical Association 106(494):746–762. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/jasa.2011.r10138")}.

Examples

# Compute the squared percentage error scoring function.

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

df$squared_relative_error <- srelerr_sf(x = df$x, y = df$y)

print(df)

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