MetricsWeighted (version 0.5.0)

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 [1]. 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,
  ...
)

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.

Value

A numeric vector of length one.

References

[1] Ehm, W., Gneiting, T., Jordan, A. and Kr<U+00FC>ger, 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>.

Examples

# NOT RUN {
elementary_score_expectile(1:10, c(1:9, 12), alpha = 0.5, theta = 11)
elementary_score_expectile(1:10, c(1:9, 12), alpha = 0.5, theta = 11, w = rep(1, 10))
elementary_score_quantile(1:10, c(1:9, 12), alpha = 0.5, theta = 11, w = rep(1, 10))
# }