Title: Adaptive estimation of multivariate piecewise constant functions
Authors: Sabyasachi Chatterjee - University of Illinois at Urbana Champaign (United States) [presenting]
Abstract: The estimation of multivariate piecewise constant functions is considered. A natural estimator is the Dyadic Cart estimator. We show that an extension of Dyadic Cart attains the best possible risk (up to log factors) adaptively for all piecewise constant functions in dimension 2. In higher dimensions, such a property continues to hold for a special subclass of all piecewise constant functions, but not all. Along the way, we show some new adaptive results for estimation of functions of bounded variation using dyadic cart and its extensions.