Gradient modeling for multivariate quantitative data |
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Authors: | Tomonari Sei |
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Institution: | (3) Dept. Math. Univ. Aegean, Karlovassi, Samos, Greece;(4) A.G. Anderson Graduate School of Management Univ. California, Riverside, California, USA |
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Abstract: | We propose a new parametric model for continuous data, a “g-model”, on the basis of gradient maps of convex functions. It
is known that any multivariate probability density on the Euclidean space is uniquely transformed to any other density by
using the gradient map of a convex function. Therefore the statistical modeling for quantitative data is equivalent to design
of the gradient maps. The explicit expression for the gradient map enables us the exact sampling from the corresponding probability
distribution. We define the g-model as a convex subset of the space of all gradient maps. It is shown that the g-model has
many desirable properties such as the concavity of the log-likelihood function. An application to detect the three-dimensional
interaction of data is investigated. |
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Keywords: | |
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