MetricsWeighted (version 0.5.4)

elementary_score: Elementary Scoring Function for Expectiles and Quantiles

Description

Weighted average of the elementary scoring function for expectiles resp. quantiles at level alpha with parameter theta, see reference below. Every choice of theta gives a scoring function consistent for the expectile resp. 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

Optional level of expectile resp. quantile.

theta

Optional parameter.

...

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)