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Abstract:
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The talk will review and present some recent developments in the estimation and inference of shape restricted functions. Shape restrictions like monotonicity, convexity, log-concavity, etc. might be a priori known in certain statistical problems and when incorporated leads to estimates that do not require specification of any tuning parameter (like bandwidth in kernel smoothing). Usually these problems exhibit non-standard asymptotics, i.e., the limit distributions of the estimates are non-normal and the rate of convergence is not root-n. We also study resampling based inference in these problems.
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