Modelling Functional Data with High-dimensional Error Structure

Abstract

We propose to model rawfunctional data as a mixture of functions and highdimensional error. The conventional approach to retrieve the functional component from raw data is through varied smoothing techniques. Nevertheless, smoothing itself may not be adequate when measurement error exists.We propose to use factor model to reduce the dimension of the high-dimensional measurement error, while smoothing the functional component. Our model also provides as an alternative for modelling functional data with step jump. Regularized least squares method is used to find the model estimates. We look at the asymptotic behaviour of the estimator when both the sample size and the number of points per curve go to infinity and the limiting distribution is derived.