Stratified incomplete local simplex tests for curvature of nonparametric multiple regression

Yanglei Song, Xiaohui Chen, Kengo Kato

Research output: Contribution to journalArticlepeer-review


Principled nonparametric tests for regression curvature in Rd are often statistically and computationally challeng-ing. 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, we develop a general theory for incomplete U-processes with stratified random sparse weights. Novel technical ingredients include maximal inequalities for the supremum of multiple incomplete U-processes.

Original languageEnglish (US)
Pages (from-to)323-349
Number of pages27
Issue number1
StatePublished - 2023


  • Nonparametric regression
  • curvature testing
  • incomplete U-processes
  • stratification

ASJC Scopus subject areas

  • Statistics and Probability


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