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

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STSW02 - Statistics of geometric features and new data types

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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