Elementary Scoring Function for Expectiles and Quantiles

Source: R/elementary_score.R

Weighted average of the elementary scoring function for expectiles or quantiles at level \(\alpha\) with parameter \(\theta\), see reference below. Every choice of \(\theta\) gives a scoring function consistent for the expectile or quantile at level \(\alpha\). Note that the expectile at level \(\alpha = 0.5\) is the expectation (mean). The smaller the score, the better.

elementary_score_expectile(
  actual,
  predicted,
  w = NULL,
  alpha = 0.5,
  theta = 0,
  ...
)

elementary_score_quantile(
  actual,
  predicted,
  w = NULL,
  alpha = 0.5,
  theta = 0,
  ...
)

Arguments

actual

Observed values.

predicted

Predicted values.

w

Optional case weights.

alpha

Level of expectile or quantile. The default alpha = 0.5 corresponds to the expectation/median.

theta

Evaluation point.

...

Further arguments passed to weighted_mean().

Value

A numeric vector of length one.

References

Ehm, W., Gneiting, T., Jordan, A. and Krüger, F. (2016), Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings. J. R. Stat. Soc. B, 78: 505-562, <doi.org/10.1111/rssb.12154>.

See also

murphy_diagram()

Examples

elementary_score_expectile(1:10, c(1:9, 12), alpha = 0.5, theta = 11)
#> [1] 0.05
elementary_score_quantile(1:10, c(1:9, 12), alpha = 0.5, theta = 11)
#> [1] 0.05