mspe {scoringfunctions} | R Documentation |
Mean squared percentage error (MSPE)
Description
The function mspe computes the mean squared percentage error when
\textbf{\textit{y}}
materialises and \textbf{\textit{x}}
is the
prediction.
Mean squared percentage error is a realised score corresponding to the squared percentage error scoring function sperr_sf.
Usage
mspe(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 squared percentage 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)/y)^{2}
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 squared percentage error.
Note
For details on the squared percentage error scoring function, see sperr_sf.
The concept of realised (average) scores is defined by Gneiting (2011) and Fissler and Ziegel (2019).
The mean squared percentage error is the realised (average) score corresponding to the squared percentage 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 squared percentage error.
set.seed(12345)
x <- 0.5
y <- rlnorm(n = 100, mean = 0, sdlog = 1)
print(mspe(x = x, y = y))
print(mspe(x = rep(x = x, times = 100), y = y))