serr_sf: Squared error scoring function

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

Squared error scoring function

Description

The function serr_sf computes the squared error scoring function when y materialises and x is the predictive mean functional.

The squared error scoring function is defined in Table 1 in Gneiting (2011).

Usage

serr_sf(x, y)

Arguments

x	Predictive mean 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) := (x - y)^2

Domain of function:

x \in \mathbb{R}

y \in \mathbb{R}

Range of function:

S(x, y) \geq 0, \forall x, y \in \mathbb{R}

Value

Vector of squared errors.

Note

For details on the squared error scoring function, see Savage (1971), Gneiting (2011).

The mean functional is the mean \textnormal{E}_F[Y] of the probability distribution F of y (Gneiting 2011).

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

The squared error scoring function is strictly \mathbb{F}-consistent for the mean functional. \mathbb{F} is the family of probability distributions F for which the second moment exists and is finite (Savage 1971; Gneiting 2011).

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")}.

Savage LJ (1971) Elicitation of personal probabilities and expectations. Journal of the American Statistical Association 66(337):783–810. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.1971.10482346")}.

Examples

# Compute the squarer error scoring function.

df <- data.frame(
    y = rep(x = 0, times = 5),
    x = -2:2
)

df$squared_error <- serr_sf(x = df$x, y = df$y)

print(df)

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