Asymptotic equivalence of functional linear regression and a white noise inverse problem

Abstract: 

We consider the statistical experiment of functional linear regression (FLR). Furthermore, we introduce a white noise model where one observes an Ito process which contains the covariance operator of the corresponding FLR model in its construction. We prove asymptotic equivalence of FLR and this white noise model in LeCam’s sense. Moreover, we show equivalence of FLR and an empirical version of the white noise model for finite sample sizes.

About the speaker: Alexander Meister is Professor of mathematical statistics in the Institute for Mathematics at University of Rostock, Germany. He was previously a postdoctoral fellow at the Australian National University in Canberra. His main research interests are nonparametric density and regression estimation, statistical inverse problems, functional data analysis and time series analysis.