Monotone Nonparametric Regression and Confidence Intervals

• Published in: Communications in statistics. Simulation and computation Vol. 39; no. 4; pp. 828 - 845
• Main Authors: Strand, Matthew, Zhang, Yu, Swihart, Bruce J.
• Format: Journal Article
• Language: English
• Published: Colchester Taylor & Francis Group 01.04.2010; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Beryllium; Bootstrap; Computer simulation; Confidence intervals; Distribution theory; Estimators; Exact sciences and technology; Iron and steel plants; Isotonic regression; Jackknife; Local polynomial regression; Mathematical analysis; Mathematical models; Mathematics; Monte Carlo methods; Monte Carlo simulation; Nonparametric inference; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Parametric inference; Probability and statistics; Regression; Sciences and techniques of general use; Statistics; Studies; 62G05; 62G08; Statistical distribution; 62G09; Non parametric estimation; Stochastic method; Least squares method; Jackknife; Bootstrap; Jackknife method; Approximation theory; Local polynomial regression; Monte Carlo method; Grid pattern; Chronic disease; Smooth estimate; Nonparametric regression; Statistical estimation; Two variables function; Confidence interval; Statistical method; Response function; Numerical analysis; Isotonic regression; Numerical simulation; Resampling method; Polynomial regression; 62G15
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610911003650367

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.