qlike: QLIKE

In scoringfunctions: Loss Functions for Assessing Point Forecasts

QLIKE

Description

The function qlike computes the QLIKE score when \textbf{\textit{y}} materialises and \textbf{\textit{x}} is the prediction.

QLIKE is a realised score corresponding to the Bregman scoring function (type 3, QLIKE scoring function) bregman3_sf.

Usage

qlike(x, y)

Arguments

x	Prediction. It can be a vector of length n (must have the same length as \textbf{\textit{y}}).
y	Realisation (true value) of process. It can be a vector of length n (must have the same length as \textbf{\textit{x}}).

Details

QLIKE 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) := (y/x) - \log(y/x) - 1

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 QLIKE.

Note

For details on the Bregman scoring function (type 3, QLIKE scoring function), see bregman3_sf.

The concept of realised (average) scores is defined by Gneiting (2011) and Fissler and Ziegel (2019).

QLIKE is the realised (average) score corresponding to the Bregman scoring function (type 3, QLIKE scoring function).

References

Fissler T, Ziegel JF (2019) Order-sensitivity and equivariance of scoring functions. Electronic Journal of Statistics 13(1):1166–1211. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/19-EJS1552")}.

Gneiting T (2011) Making and evaluating point forecasts. Journal of the American Statistical Association 106(494):746–762. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/jasa.2011.r10138")}.

See Also

bregman3_sf, mean_if

Examples

# Compute QLIKE.

set.seed(12345)

x <- 0.5

y <- rlnorm(n = 100, meanlog = 0, sdlog = 1)

print(qlike(x = x, y = y))

print(qlike(x = rep(x = x, times = 100), y = y))

scoringfunctions documentation built on Aug. 30, 2026, 5:07 p.m.