Confidence intervals in monotone regression
针对单调回归函数，提出基于平滑最小二乘估计的bootstrap置信区间，解决了普通bootstrap不一致的问题，并给出自动带宽选择方法。
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) , is inconsistent in this situation. We show that an ‐consistent bootstrap can be based on the smoothed , 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).