Project Grant 2210504

This three-year National Science Foundation project grant of $350,000 supports research at the University of California, Berkeley to develop novel nonparametric estimation methodologies under mixed derivative smoothness constraints. The investigator plans to expand methodology for nonparametric regression allowing restricted interaction orders, design faster algorithms, and prove theoretical accuracy results under more general assumptions. The possibility of near parametric rates under strong sparsity settings will be explored using tensor product bases including complex exponentials and radial basis functions. Uncertainty quantification using Bayesian approaches with a focus on Cauchy priors will also be systematically explored. New mixed derivative approaches for shape-constrained regression problems including those based on entire monotonicity with restricted interactions and total Popoviciu convexity will be developed. Mixed derivative methodologies for spectral density estimation of time series and density estimation will be studied as well. The funding falls under the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049), which supports strengthening the nation's scientific enterprise through increasing mathematical and physical sciences knowledge and understanding major national problems.