Achieving Spatial Adaptation via Inconstant Penalization: Theory and Computational Strategies

研究者将研究不恒定惩罚与局部适应性之间的关系。目标是在底层模型（响应和输入变量之间的关系）具有非均匀粗糙度时实现位置自适应函数估计。研究者将(1)量化变量惩罚函数与结果局部自适应之间的联系，(2)推广高维输入变量的方法，(3)研究算法参数的选择，(4)推导结果估计器的理论性质，(5)设计快速计算策略。非齐次粗糙条件下的泛函估计是许多统计应用中的一个基本问题。这项研究将有助于对这些问题的基本理解，并提供可部署的工具。特别是对于大型数据集，预期比当前最先进的方法有更好的性能。

The investigator will study the relation between inconstant penalization and local adaptivity. The goal is to achieve location adaptive functional estimation when the underlying model (of the relation between a response and input variables) has inhomogeneous roughness. The investigator will (1) quantify the connection between a variable penalty function and the resulting local adaptivity, (2) generalize the methods for high-dimensional input variables, (3) study the selection of algorithmic parameters, (4) derive theoretical properties of the resulting estimators, and (5) design fast computational strategies.Functional estimation under inhomogeneous roughness is a fundamental problem in many statistical applications. This study will contribute to the fundamental understanding to these problems, as well as providing deployable tools. Especially for large size datasets, better performance than the current state-of-the-art methodology is anticipated.