Prediction in Measurement Error Models

• Activity Number: 145
• Type: Invited
• Date/Time: Monday, August 3, 2009 : 10:30 AM to 12:20 PM
• Sponsor: JASA, Theory and Methods
• Author(s): Raymond J. Carroll and Aurore Delaigle*+ and Hall Peter
• Companies: Texas A&M University and University of Bristol and The University of Melbourne
• Keywords: nonparametric ; regression ; rates of convergence ; nutrition ; epidemiology

Abstract

Predicting Y from a future X based on data (X_i,Y_i) is a fundamental inference problem. When X is observed accurately, the problem is that of standard regression estimation of E(Y|X). When the data X_i and future X are measured with error, prediction is sometimes less standard. With W denoting the future X measurement, prediction of Y requires estimation of E(Y|W). This is complicated when measurements are made under different conditions, so that errors in X_i and X are not identically distributed. We study this problem nonparametrically showing that convergence rates of estimators of E(Y|W) can vary from root-n to much slower nonparametric rates. We develop highly-adaptive, data-driven methods that perform well as illustrated by an interesting application in nutritional epidemiology. We review recent results in nonparametric measurement error methods as background to our work.