Search results for "Signed measure"
showing 2 items of 2 documents
On a representation theorem for finitely exchangeable random vectors
2016
A random vector $X=(X_1,\ldots,X_n)$ with the $X_i$ taking values in an arbitrary measurable space $(S, \mathscr{S})$ is exchangeable if its law is the same as that of $(X_{\sigma(1)}, \ldots, X_{\sigma(n)})$ for any permutation $\sigma$. We give an alternative and shorter proof of the representation result (Jaynes \cite{Jay86} and Kerns and Sz\'ekely \cite{KS06}) stating that the law of $X$ is a mixture of product probability measures with respect to a signed mixing measure. The result is "finitistic" in nature meaning that it is a matter of linear algebra for finite $S$. The passing from finite $S$ to an arbitrary one may pose some measure-theoretic difficulties which are avoided by our p…
A multicriteria extension of the efficient market hypothesis
2021
Challenging the Efficient Market Hypothesis (EMH) has been a recurrent topic for researchers and practitioners since its formulation. Hundreds of empirical studies claim to either prove or disprove the EMH by means of a number of heterogeneous methods. Even though the EMH is usually adjusted to a measure of risk, there is a lack of a formal analysis within a multiple-criteria context. In this paper, we propose a extension of the EMH that accommodates the foundations of multiple-criteria decision analysis. To this end, we rely on a family of parametric signed dissimilarity measures to assess multidimensional performance differences. Since normalization is a critical step in our approach to a…