huber_sf {scoringfunctions} | R Documentation |
Huber scoring function
Description
The function huber_sf computes the Huber scoring function with parameter
, when
materializes and
is the predictive Huber mean.
The Huber scoring function is defined in Huber (1964).
Usage
huber_sf(x, y, a)
Arguments
x |
Predictive Huber mean (prediction). It can be a vector of length
|
y |
Realization (true value) of process. It can be a vector of length
|
a |
It can be a vector of length |
Details
The Huber scoring function is defined by:
Domain of function:
Range of function:
Value
Vector of Huber losses.
Note
For the definition of Huber mean, see Taggart (2022).
The Huber scoring function is negatively oriented (i.e. the smaller, the better).
The Huber scoring function is strictly consistent for the Huber mean relative to
the family of potential probability distributions
for
the future
for which
and
exist and are finite (Taggart 2022).
References
Huber PJ (1964) Robust Estimation of a Location Parameter. Annals of Mathematical Statistics 35(1):73–101. doi:10.1214/aoms/1177703732.
Taggart RJ (2022) Point forecasting and forecast evaluation with generalized Huber loss. Electronic Journal of Statistics 16:201–231. doi:10.1214/21-EJS1957.
Examples
# Compute the Huber scoring function.
df <- data.frame(
x = c(-3, -2, -1, 0, 1, 2, 3),
y = c(0, 0, 0, 0, 0, 0, 0),
a = c(2.7, 2.5, 0.6, 0.7, 0.9, 1.2, 5)
)
df$huber_penalty <- huber_sf(x = df$x, y = df$y, a = df$a)
print(df)