A simple integral representation of single-event scoring rules
Alexander R. Pruss
Abstract
A simple integral representation involving no derivatives or continuity assumptions is given for proper single-event scoring rules.
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A simple integral representation of single-event scoring rules
Authors
Abstract
A simple integral representation involving no derivatives or continuity assumptions is given for proper single-event scoring rules.
Paper Structure (5 theorems, 26 equations)
This paper contains 5 theorems, 26 equations.
Key Result
Theorem 1
Let $T:[0,1]\to[-\infty,\infty)$ be monotonic non-decreasing and finite on $(0,1)$. Fix any real constant $C$ and any $c\ge 0$. Let for $x<1$. If $T$ is continuous at $1$, let $F(1)=-c+\lim_{x\to 1-} F(x)$, and otherwise let $F(1)=-\infty$. Then the limit is defined if $T$ is continuous at $1$, and in any case $(T,F)$ is proper. Conversely, any function $F$ on $[0,1]$ that is finite except perhap
Theorems & Definitions (7)
- Theorem 1
- Corollary 1
- Corollary 2
- Corollary 3
- Lemma 1
- proof
- proof : Proof of Theorem \ref{['thm:repr']}