Prediction in measurement error models

Abstract: 

Predicting Y from a future X based on data (Xi, Yi) 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 Xi 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 Xi 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.

About the speaker: Aurore Delaigle is Associate Professor at the Department of Mathematics and Statistics of the University of Melbourne. She currently holds a Queen Elizabeth II Fellowship and concentrates on her research on deconvolution problems, functional data analysis and high dimensional problems.