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Adaptive Confidence Bands for Shape-Restricted Regression in Multi-dimension using Multiscale Tests

Presented by: 
Bodhisattva Sen
Monday 19th March 2018 - 13:30 to 14:30
INI Seminar Room 1
Co-author: Pratyay Datta (Columbia University)

We consider a multidimensional (continuous) Gaussian white noise regression model. We define suitable multiscale tests in this scenario. Utilizing these tests we construct confidence bands for the underlying regression function with guaranteed coverage probability, assuming that the underlying function is isotonic or convex. These confidence bands are shown to be asymptotically optimal in an appropriate sense. Computational issues will also be discussed.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons