Achieving Spatial Adaptation via Inconstant Penalization: Theory and Computational Strategies

研究者将研究非恒定惩罚与局部适应性之间的关系。我们的目标是实现位置自适应功能估计时的基础模型（响应和输入变量之间的关系）具有不均匀的粗糙度。研究者将（1）量化变量罚函数和所得局部自适应性之间的联系，（2）推广高维输入变量的方法，（3）研究算法参数的选择，（4）推导所得估计量的理论性质，非齐次粗糙度下的函数估计是许多统计应用中的基本问题。本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。特别是对于大规模的数据集，更好的性能比目前最先进的方法是预期的。

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.