elementary_score: Elementary Scoring Function for Expectiles and Quantiles

In MetricsWeighted: Weighted Metrics and Performance Measures for Machine Learning

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,
  ...
)

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

MetricsWeighted documentation built on Nov. 16, 2023, 5:09 p.m.