Department of Statistics Seminar
North Carolina State University

presents

Tony Cai

Department of Statistics

The Wharton School

University of Pennsylvania

Functional Data Analysis: Prediction and Adaptive Estimation
 
Abstract
 

Functional data arises commonly in different fields of applied sciences including, for example, chemometrics, medicine, and econometrics. There has been substantial recent work on methods for estimating the slope function in functional linear model. In this talk we consider both prediction and adaptive estimation in functional linear regression. We show that the prediction problem has very different characteristics as the slope-function estimation problem. While the latter is intrinsically nonparametric, the former can be either nonparametric or semiparametric. More generally, the rate of convergence of the predicted value of the mean response in the regression model, given a particular value of the explanatory variable, is determined by a subtle interaction among the smoothness of the predictand, of the slope function in the model, and of the covariance function for the distribution of explanatory variables.

We also consider adaptive estimation of the slope function. An adaptive estimator is constructed using functional principal component analysis and block thresholding. The procedure is shown to adaptively attain the optimal rate of convergence over a large collection of function spaces.

Time permitting; classification with functional data will also be discussed in the context of chemical identification.

Friday, October 3, 2008
3:35 - 4:35 pm
321 Riddick Hall

Refreshments will be served in the common area of Riddick at 3:00 pm.

NOTE: No food or drink is allowed in any of the classrooms in Riddick Hall.