scoringfunctions (version 1.1)

mean_if: Mean identification function

Description

The function mean_if computes the mean identification function , when \(y\) materialises and \(x\) is the predictive mean.

The mean identification function is defined in Table 9 in Gneiting (2011).

Usage

mean_if(x, y)

Value

Vector of values of the mean identification function.

Arguments

x

Predictive mean (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 mean identification function is defined by:

$$V(x, y) := x - y$$

Domain of function:

$$x \in \mathbb{R}$$

$$y \in \mathbb{R}$$

Range of function:

$$V(x, y) \in \mathbb{R}$$

References

Dimitriadis T, Fissler T, Ziegel JF (2024) Osband's principle for identification functions. Statistical Papers 65:1125--1132. tools:::Rd_expr_doi("10.1007/s00362-023-01428-x").

Fissler T, Ziegel JF (2016) Higher order elicitability and Osband's principle. The Annals of Statistics 44(4):1680--1707. tools:::Rd_expr_doi("10.1214/16-AOS1439").

Gneiting T (2011) Making and evaluating point forecasts. Journal of the American Statistical Association 106(494):746--762. tools:::Rd_expr_doi("10.1198/jasa.2011.r10138").

Newey WK, Powell JL (1987) Asymmetric least squares estimation and testing. Econometrica 55(4):819--847. tools:::Rd_expr_doi("10.2307/1911031").

Examples

# Compute the mean identification function.

df <- data.frame(
    y = rep(x = 0, times = 3),
    x = c(-2, 0, 2)
)

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