We consider several problems in areas where Michael Woodroofe has made seminal contributions to. In higher criticism, we develop a one-sided sequential probability ratio test based on the ordered p-values to achieve optimal detection of rare and weak signals. This makes an interesting connection to the test of power one and nonlinear renewal theorem. In multiple isotonic regression, a block estimator is developed to attain minimax rate for a wide range of signal-to-noise ratio, to achieve adaptation to the parametric root-n rate up to a logarithmic factor in the case where the unknown mean is piecewise constant, and to achieve adaptation in variable selection. In uncertainty quantification, we develop second order Stein formulas for statistical inference in nonparametric and high-dimensional problems. Applications of the second order Stein method include exact formulas and upper bounds for the variance of risk estimators and risk bounds for regularized or shape constrained estimators and related degrees of freedom adjustments and confidence regions.

*Hors d'oeuvres immediately following in 337 West Hall (Don Meyer Commons)