Confidence intervals in monotone regression

Piet Groeneboom and Geurt Jongbloed

Scandinavian Journal of Statistics, 2024, vol. 51, issue 4, 1749-1781

Abstract: 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).

Date: 2024
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