Confidence intervals in monotone regression

2023/03/31 by Groeneboom, Piet, Jongbloed, Geurt
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2303.17988

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, however, that a 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). The procedure is illustrated using a well known dataset related to climate change.

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