Estimation and inference for minimizer and minimum of convex functions: Optimality, adaptivity and uncertainty principles
凸函数极小点与最小值的估计和推断：最优性、自适应性与不确定性原理
Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a procedure is evaluated at individual functions. Fully adaptive and computationally efficient algorithms are proposed and sharp minimax lower bounds are given for both the estimation accuracy and expected length of confidence intervals for…