mre {scoringfunctions} | R Documentation |
Mean relative error (MRE)
Description
The function mre computes the mean relative error when \textbf{\textit{y}}
materialises and \textbf{\textit{x}}
is the prediction.
Mean relative error is a realised score corresponding to the relative error scoring function relerr_sf.
Usage
mre(x, y)
Arguments
x |
Prediction. It can be a vector of length |
y |
Realisation (true value) of process. It can be a vector of length
|
Details
The mean relative error is defined by:
S(\textbf{\textit{x}}, \textbf{\textit{y}}) := (1/n)
\sum_{i = 1}^{n} L(x_i, y_i)
where
\textbf{\textit{x}} = (x_1, ..., x_n)^\mathsf{T}
\textbf{\textit{y}} = (y_1, ..., y_n)^\mathsf{T}
and
L(x, y) := |(x - y)/x|
Domain of function:
\textbf{\textit{x}} > \textbf{0}
\textbf{\textit{y}} > \textbf{0}
where
\textbf{0} = (0, ..., 0)^\mathsf{T}
is the zero vector of length n
and the symbol >
indicates pairwise
inequality.
Range of function:
S(\textbf{\textit{x}}, \textbf{\textit{y}}) \geq 0,
\forall \textbf{\textit{x}}, \textbf{\textit{y}} > \textbf{0}
Value
Value of the mean relative error.
Note
For details on the relative error scoring function, see relerr_sf.
The concept of realised (average) scores is defined by Gneiting (2011) and Fissler and Ziegel (2019).
The mean relative error is the realised (average) score corresponding to the relative error scoring function.
References
Fissler T, Ziegel JF (2019) Order-sensitivity and equivariance of scoring functions. Electronic Journal of Statistics 13(1):1166–1211. doi:10.1214/19-EJS1552.
Gneiting T (2011) Making and evaluating point forecasts. Journal of the American Statistical Association 106(494):746–762. doi:10.1198/jasa.2011.r10138.
Examples
# Compute the mean relative error.
set.seed(12345)
x <- 0.5
y <- rlnorm(n = 100, mean = 0, sdlog = 1)
print(mre(x = x, y = y))
print(mre(x = rep(x = x, times = 100), y = y))