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Learn advanced statistical methods for density estimation through this 33-minute conference talk exploring shape-constrained approaches using Wasserstein projection techniques. Discover how optimal transport theory applies to statistical estimation problems, with particular focus on incorporating geometric constraints into density estimation procedures. Examine the mathematical foundations of Wasserstein projections and their role in maintaining desired shape properties while estimating probability densities from data. Explore the theoretical properties of these estimators, including convergence rates and computational considerations. Gain insights into practical applications where shape constraints are naturally imposed, such as monotonicity, convexity, or other geometric properties in statistical modeling. Understand how this approach connects optimal transport theory with nonparametric statistics, providing a principled framework for incorporating prior knowledge about density shapes into estimation procedures.
