Likelihood Ratio Tests and Confidence Intervals Based on the Shape Constraint of Concavity

• Activity Number: 306 - Algorithmic and Inferential Advances in Univariate and Multivariate Tuning-Parameter-Free Nonparametric Procedures
• Type: Topic Contributed
• Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Charles Doss* and Jon Wellner
• Companies: University of Minnesota and University of Washington
• Keywords: tests; confidence intervals; nonparametric; shape constraint; convexity

Abstract

Forming hypothesis tests or confidence intervals in nonparametric function estimation settings is generally challenging because of the need to handle unknown nuisance parameters (often related to the function's curvature). We consider several problems based on the shape constraint of convexity and propose to use likelihood ratio statistics to form hypothesis tests (which can be inverted to form confidence intervals). Our statistics are tuning parameter free, a rarity in nonparametric settings, and they are also asymptotically pivotal. Thus, they have universal critical values not depending on any unknown parameters, allowing the tests or intervals to be computed in practice.