Estimating mean dimensionality of ANOVA decompositions
نویسندگان
چکیده
The analysis of variance is now often applied to functions defined on the unit cube, where it serves as a tool for the exploratory analysis of functions. The mean dimension of a function, defined as a natural weighted combination of its ANOVA mean squares, provides one measure of how hard or easy the function is to integrate by quasi-Monte Carlo sampling. This paper presents some new identities relating the mean dimension, and some analogously defined higher moments, to the variable importance measures of Sobol’ (1993). As a result we are able to measure the mean dimension of certain functions arising in computational finance. We produce an unbiased and non-negative estimate of the variance contribution of the highest order interaction, which avoids the cancellation problems of previous estimates. In an application to extreme value theory, we find
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