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Adityanand Guntuboyina contributed to risk bounds for isotonic regression with Sabyasachi Chatterjee and Bodhisattva Sen. They quantified how the error of the monotone least-squares estimator depends on the shape of the true sequence. Nearly flat signals permit faster estimation than uniformly increasing signals, an example of adaptation to structure without specifying that structure in advance.^[ref]

Bodhisattva Sen coauthored improved risk bounds for isotonic regression with Sabyasachi Chatterjee and Adityanand Guntuboyina. Their analysis shows that the least-squares estimator adapts to the number of constant pieces of a monotone signal. The work also provides local minimax lower bounds, helping distinguish an estimator's limitations from limitations inherent in the data.^[ref]

By Sabyasachi Chatterjee, Adityanand Guntuboyina, Bodhisattva Sen.

Author-hosted preprint dated 13 November 2013, title as on this version. Introduction equations (5)–(6): isotonic LSE risk upper bound and flat-signal behavior; Section 4.1, Theorem 4.3: Gaussian local minimax lower bound around uniformly increasing sequences. Later versions use a different title; keep the cited-version identity.