论文标题
分层不完整的本地单纯形测试非参数多重回归的曲率
Stratified incomplete local simplex tests for curvature of nonparametric multiple regression
论文作者
论文摘要
在$ \ mathbb {r}^{d} $中，对回归曲率的原理非参数测试通常在统计上和计算上具有挑战性。本文介绍了分层不完整的局部单纯形（SILS）测试，以实现非参数多重回归的关节凹度。证明具有合适的自举校准的SILS测试可同时保证无维度的计算复杂性，均匀误差尺寸的多项式衰减以及一般（全局和本地）替代方案的功率一致性。为了建立这些结果，开发了一种不完整的$ U $ - 过程的一般理论，具有分层随机稀疏权重。新颖的技术成分包括多个不完整的$ u $ - 过程的最高不平等现象。
Principled nonparametric tests for regression curvature in $\mathbb{R}^{d}$ are often statistically and computationally challenging. This paper introduces the stratified incomplete local simplex (SILS) tests for joint concavity of nonparametric multiple regression. The SILS tests with suitable bootstrap calibration are shown to achieve simultaneous guarantees on dimension-free computational complexity, polynomial decay of the uniform error-in-size, and power consistency for general (global and local) alternatives. To establish these results, a general theory for incomplete $U$-processes with stratified random sparse weights is developed. Novel technical ingredients include maximal inequalities for the supremum of multiple incomplete $U$-processes.
