Adaptive Inference in Multivariate Nonparametric Regression Models Under Monotonicity

Abstract

We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a Hölder class and is assumed to be monotone with respect to some or all of the arguments. We derive the minimax rate of convergence for confidence intervals (CIs) that adapt to the underlying smoothness, and provide an adaptive inference procedure that obtains this minimax rate. The procedure differs from that of Cai and Low (2004), intended to yield shorter CIs under practically relevant specifications. The proposed method applies to general linear functionals of the regression function, and is shown to have favorable performance compared to existing inference procedures.

arXiv comment52 pages

References in corpus (5)

• On adaptive inference and confidence bands
• Confidence sets for nonparametric wavelet regression
• Adaptive confidence intervals for regression functions under shape constraints
• Minimax and Adaptive Inference in Nonparametric Function Estimation
• Confidence intervals for multiple isotonic regression and other monotone models

Cited by in corpus (1)

• Inference in Regression Discontinuity Designs under Monotonicity