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 under known design distribution. Moreover, we show equivalence of FLR and an empirical version of the white noise model for finite sample sizes. As an application, we derive sharp minimax constants in the FLR model which are still valid in the case of unknown design distribution.

arXiv commentPublished in at http://dx.doi.org/10.1214/10-AOS872 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (9)

• Functional linear regression analysis for longitudinal data
• Generalized functional linear models
• Prediction in functional linear regression
• Methodology and convergence rates for functional linear regression
• Smoothing splines estimators for functional linear regression
• Thresholding Projection Estimators in Functional Linear Models
• Adaptive functional linear regression
• Recovering convex boundaries from blurred and noisy observations
• Asymptotic approximation of nonparametric regression experiments with unknown variances

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