linex_sf {scoringfunctions} | R Documentation |
LINEX scoring function
Description
The function linex_sf computes the LINEX scoring function with parameter a
when y
materialises and x
is the predictive
-(1/a) \log{\textnormal{E}_F[\textnormal{e}^{-a Y}]}
moment generating
functional.
The LINEX scoring function is defined by Varian (1975).
Usage
linex_sf(x, y, a)
Arguments
x |
Predictive |
y |
Realisation (true value) of process. It can be a vector of length
|
a |
It can be a vector of length |
Details
The LINEX scoring function is defined by:
S(x, y, a) := \textnormal{e}^{a (x - y)} - a (x - y) - 1
Domain of function:
x \in \mathbb{R}
y \in \mathbb{R}
a \neq 0
Range of function:
S(x, y, a) \geq 0, \forall x, y \in \mathbb{R}, a \neq 0
Value
Vector of LINEX losses.
Note
For details on the LINEX scoring function, see Varian (1975) and Zellner (1986).
The LINEX scoring function is negatively oriented (i.e. the smaller, the better).
The LINEX scoring function is strictly \mathbb{F}
-consistent for
the -(1/a) \log{\textnormal{E}_F[\textnormal{e}^{-a Y}]}
moment generating
functional. \mathbb{F}
is the family of probability distributions F
for which \textnormal{E}_F[\textnormal{e}^{-a Y}]
and
\textnormal{E}_F[Y]
exist and are finite (Varian 1975; Zellner 1986;
Gneiting 2011).
References
Gneiting T (2011) Making and evaluating point forecasts. Journal of the American Statistical Association 106(494):746–762. doi:10.1198/jasa.2011.r10138.
Varian HR (1975) A Bayesian approach to real estate assessment. In: Fienberg SE, Zellner A(eds) Studies in Bayesian Econometrics and Statistics in Honor of Leonard J. Savage. Amsterdam: North-Holland, pp 195–208.
Zellner A (1986) Bayesian estimation and prediction using asymmetric loss functions. Journal of the American Statistical Association 81(394):446–451. doi:10.1080/01621459.1986.10478289.
Examples
# Compute the LINEX scoring function.
df <- data.frame(
y = rep(x = 2, times = 3),
x = 1:3,
a = c(-1, 1, 2)
)
df$linex_loss <- linex_sf(x = df$x, y = df$y, a = df$a)
print(df)