Abstract
The representation of multivariate functions is often given by means of functional ANOVA, in particular in Statistics, Simulation and Sensitivity Analysis. In despite of such use, its analytic and geometric properties have not been addressed yet. We derive conditions for continuity, differentiability, monotonicity and ultramodularity properties in functional ANOVA. We study the implications of these findings in multiattribute utility theory. We establish the conditions under which analytic properties of a multiattribute utility function imply the same properties of its one-attribute functions. The converse implications are also investigated.
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