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Title: Convolution on networks Authors:  Andrii Babii - University of North Carolina (United States)
Jean-Pierre Florens - Toulouse School of Economics (France) [presenting]
Abstract: A concept of convolution on possibly discrete or continuous network is defined where the interdependence structure is characterized by a Laplacian operator. This operator determines a concept of Fourier transform and then a convolution and we concentrate our attention to linear models where the link between parameter and explanatory variable is a convolution. Regularized estimations using instrumental variables are proposed and their properties are studied. Several example are given: finite network, locally compact groups, minimum manifolds.