Confidence intervals in monotone regression

We construct bootstrap confidence intervals for a monotone regression function. It has been shown that the ordinary nonparametric bootstrap, based on the nonparametric least squares estimator (LSE) f^n, is inconsistent in this situation. We show that an n2/5‐consistent bootstrap can be based on the...

Full description

Saved in:
Bibliographic Details
Published in:Scandinavian journal of statistics 2024-12, Vol.51 (4), p.1749-1781
Main Authors: Groeneboom, Piet, Jongbloed, Geurt
Format: Article
Language:English
Subjects:
Asymptotic methods
bandwidth choice
confidence intervals
Nadaraya Watson
smooth monotone regression
smoothed bootstrap
Statistical analysis
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We construct bootstrap confidence intervals for a monotone regression function. It has been shown that the ordinary nonparametric bootstrap, based on the nonparametric least squares estimator (LSE) f^n, is inconsistent in this situation. We show that an n2/5‐consistent bootstrap can be based on the smoothed f^n, to be called the SLSE (Smoothed Least Squares Estimator). The asymptotic pointwise distribution of the SLSE is derived. The confidence intervals, based on the smoothed bootstrap, are compared to intervals based on the (not necessarily monotone) Nadaraya Watson estimator and the effect of Studentization is investigated. We also give a method for automatic bandwidth choice, correcting work in Sen and Xu (2015). Analogous methods for constructing confidence intervals in the current status model are discussed, improving on work in Groeneboom and Hendrickx (2018).
ISSN:0303-6898
1467-9469
DOI:10.1111/sjos.12730