Monotone Nonparametric Regression and Confidence Intervals

Several variations of monotone nonparametric regression have been developed over the past 30 years. One approach is to first apply nonparametric regression to data and then monotone smooth the initial estimates to “iron out” violations to the assumed order. Here, such estimators are considered, where local polynomial regression is first used, followed by either least squares isotonic regression or a monotone method using simple averages. The primary focus of this work is to evaluate different types of confidence intervals for these monotone nonparametric regression estimators through Monte Carlo simulation. Most of the confidence intervals use bootstrap or jackknife procedures. Estimation of a response variable as a function of two continuous predictor variables is considered, where the estimation is performed at the observed values of the predictors (instead of on a grid). The methods are then applied to data involving subjects that worked at plants that use beryllium metal who have developed chronic beryllium disease.