MetricsWeighted (version 1.0.4)

elementary_score: Elementary Scoring Function for Expectiles and Quantiles

Description

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.

Usage

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

Value

A numeric vector of length one.

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().

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)
elementary_score_quantile(1:10, c(1:9, 12), alpha = 0.5, theta = 11)